Question: Is the Granville Sharp Rule in effect in Titus 2:13 and 2 Peter 1:1? What evidence supports and/or refutes the use of this rule as applied to the similar clause in both of these texts?
One very significant reason is the well regarded advanced Greek grammar Blass-Debrunner-Funk (BDF)
It is frequently quoted by scholars, and there is really no substitute for it. Here is an entry for Titus 2:13 in section 276.3.
276.3 (3) Cf. 2 P 1:1 (but here S has κυρίου for θεοῦ, probably correctly; cf. 11, 2: 20, 3: 2, 18); however σωτῆρος ἡμ. ̓Ι.Χρ. may be taken by itself and separated from the preceding (cf. §268(2) for the omission of the art. elsewhere). Cf. W.-S. § 18, 7d(!); Mlt. 84 [134f.]; A. T. Robertson, The Greek Article and the Deity of Christ (Exp. VIII 21 [1921] 182–8).
(A Greek Grammar of the New Testament and Other Early Christian Literature. Chicago, Illinois: Cambridge at the University Press, The Uniiversity of Chicago Press, BDF, 1961)
After citing the reading in manuscript S10 where “Lord” is found and not “God,” BDF concludes that even without the variant “Lord and Savior,” “σωτῆρος ἡμ. ̓Ι. Χρ. may be taken by itself and separated from the preceding.”
The preceding “God” in other readings would thus not identify Jesus as “God” for the grammatical reasons that titles such as this are definite even with the omission of the article. BDF §268(2) and WS. §18, 7d are given in support of this conclusion.
See Winer-Schmiedel Grammatik §18 below that is quoted at BDF 276.3. It mentions both 2 Peter 1:1 and Titus 2:13.
Note that τοῦ θεοῦ ἡμῶν καὶ σωτῆρος Ἰησοῦ Χριστοῦ from Winer-Schmiedel uses the same reading as our modern critical editions such as the Nestle-Aland 28th edition,

If the second substantive at Titus 2:13 and 2 Peter 1:1 are definite as BDF suggests, both verses have two persons in view and even Granville Sharp's rule does not apply.
Excursus of BDAG on θεός
How does one describe the entry in BDAG for θεός when used with reference to Christ?
One must remember that BDAG is the third edition of the Bauer lexicon translated from German to English. Much in BDAG is from the 1975 BAG and the 1985 BAGD.
The entry for Titus 2:13 in the article on θεός when used of Christ is from the earlier editions. It simply says says:
Tit 2:13 (μέγας θ.). [a]
At first glance this looks like a solid endorsement for calling Christ “great God.”
However it is wise to read the way BDAG characterizes the different verses where some say θεός is used of Christ and why.
It starts with:
BDAG θεος 2. Some writings in our lit. use the word θ. w. ref. to Christ** (without necessarily equating Christ with the Father, and therefore in harmony w. the Shema of Israel Dt 6:4; cp. Mk 10:18 and 4a below), though the interpretation of some of the pass. is in debate.
Some passages are in “debate” and some are not.
What does BDAG mean when θεός is used of Christ?
In Mosaic and Gr-Rom. traditions the fundamental semantic component in the understanding of deity is the factor of performance**, namely saviorhood or extraordinary contributions to one’s society. Dg. 10:6 defines the ancient perspective: ὃς ἃ παραὰτοῦ θεοῦ λάβων ἔχει, τα τα ῦ το ςῖ ἐπιδεομένοις χορηγ ν ῶ , θεοὰς γίνεται τν ῶ λαμβανάντων ** one who ministers to the needy what one has received from God proves to be a god to the recipients
So Christ is “a god .” How does BDAG indicate a verse that calls Christ θεός is not debatable?
John 1:1 is an example of this. It certainly refers to Christ here!
In any event, θ. certainly refers to Christ, as one who manifests primary characteristics of deity, in the foll. NT pass.: J 1:1b (w. ὁ θεός 1:1a, which refers to God in the monotheistic context of Israel’s tradition.
But note BDAG contrasts θεός at 1:1b with its use at ὁ θεός 1:1a which is “God in the monotheistic context of Israel’s tradition.”
With this in mind consider that in the year 2000 Danker added a qualification to θεός at Titus 2:13 based on the use of και that was not in BAG or BAGD.
BDAG σωτηρ - ὁ μέγας θεὸς καὶ σ. ἡμῶν Χρ. Ἱ. our great God and Savior Christ Jesus Tit 2:13 (cp. PLond III, 604b, 118 p. 80 [47 AD] τῷ μεγάλῳ θεῷ σωτῆρι; but the presence of καί Tit 2:13 suggests a difft. semantic aspect and may justify the rendering in NRSV mg)
So, the latest scholarship of Danker moves away from the earlier entry which was not a strong endorsement in the first place.
When coupled with the entry for Σωτηρ above, BDAG is certainly mixed in this verse, but the latest addition is based on linguistics and gives the reason for the addition.
In any event, if BDAG applies θεός to Christ at Titus 2:13 it is not dogmatic and with the understanding that it is not a monotheistic use of θεός as used at John 1:1a.
[a] BDAG θεος 2. Some writings in our lit. use the word θ. w. ref. to Christ (without necessarily equating Christ with the Father, and therefore in harmony w. the Shema of Israel Dt 6:4; cp. Mk 10:18 and 4a below), though the interpretation of some of the pass. is in debate. In Mosaic and Gr-Rom. traditions the fundamental semantic component in the understanding of deity is the factor of performance, namely saviorhood or extraordinary contributions to one’s society. Dg. 10:6 defines the ancient perspective: ὃς ἃ παραὰτοῦ θεοῦ λάβων ἔχει, τα τα ῦ το ςῖ ἐπιδεομένοις χορηγ ν ῶ , θεοὰς γίνεται τν ῶ λαμβανάντων ** one who ministers to the needy what one has received from God proves to be a god to the recipients (cp. Sb III, 6263, 27f of a mother). Such understanding led to the extension of the mng. of θ. to pers. who elicit special reverence (cp. pass. under 4 below; a similar development can be observed in the use of σέβομαι and cognates). In Ro 9:5 the interpr. is complicated by demand of punctuation marks in printed texts. If a period is placed before ὁ ὢν κτλ., the doxology refers to God as defined in Israel (so EAbbot, JBL 1, 1881, 81-154; 3, 1883, 90-112; RLipsius; HHoltzmann, Ntl. Theol.2 II 1911, 99f; EGünther, StKr 73, 1900, 636-44; FBurkitt, JTS 5, 1904, 451-55; Jülicher; PFeine, Theol.d. NTs6 ’34, 176 et al.; RSV text; NRSV mg.). A special consideration in favor of this interpretation is the status assigned to Christ in 1 Cor 15:25-28 and the probability that Paul is not likely to have violated the injunction in Dt 5:7.—If a comma is used in the same place, the reference is to Christ (so BWeiss; EBröse, NKZ 10, 1899, 645-57 et al.; NRSV text; RSV mg. S. also ε1.—Undecided: THaering.—The transposition by the Socinian scholar JSchlichting [died 1661] ὧν ὁ‘to whom belongs’ was revived by JWeiss, D. Urchristentum 1917, 363; WWrede, Pls 1905, 82; CStrömman, ZNW 8, 1907,319f). In 2 Pt 1:1; 1J 5:20 the interpretation is open to question (but cp. ISmyrna McCabe .0010, 100 ὁ θεοὰς καιὰσωτηὰρ Ἀντίοχος). In any event, θ. certainly refers to Christ, as one who manifests primary characteristics of deity, in the foll. NT pass.: J 1:1b (w. ὁ θεός 1:1a, which refers to God in the monotheistic context of Israel’s tradition. On the problem raised by such attribution s. J 10:34 [cp. Ex 7:1; Ps 81:6]; on θεός w. and without the article, acc. to whether it means God or the Logos, s. Philo, Somn. 1, 229f; JGriffiths, ET 62, ’50/51, 314-16; BMetzger, BDAG θεος 2. Some writings in our lit. use the word θ. w. ref. to Christ** (without necessarily equating Christ with the Father, and therefore in harmony w. the Shema of Israel Dt 6:4; cp. Mk 10:18 and 4a below), though the interpretation of some of the pass. is in debate. In Mosaic and Gr-Rom. traditions the fundamental semantic component in the understanding of deity is the factor of performance, namely saviorhood or extraordinary contributions to one’s society. Dg. 10:6 defines the ancient perspective: ὃς ἃ παραὰτοῦ θεοῦ λάβων ἔχει, τα τα ῦ το ςῖ ἐπιδεομένοις χορηγ νῶ θεοὰς γίνεται τν ῶ λαμβανάντων ** one who ministers to the needy what one has received from God proves to be a god to the recipients (cp. Sb III, 6263, 27f of a mother). Such understanding led to the extension of the mng. of θ. to pers. who elicit special reverence (cp. pass. under 4 below; a similar development can be observed in the use of σέβομαι and cognates). In Ro 9:5 the interpr. is complicated by demand of punctuation marks in printed texts. If a period is placed before ὁ ὢν κτλ., the doxology refers to God as defined in Israel (so EAbbot, JBL 1, 1881, 81-154; 3, 1883, 90-112; RLipsius; HHoltzmann, Ntl. Theol.2 II 1911, 99f; EGünther, StKr 73, 1900, 636-44; FBurkitt, JTS 5, 1904, 451-55; Jülicher; PFeine, Theol.d. NTs6 ’34, 176 et al.; RSV text; NRSV mg.). A special consideration in favor of this interpretation is the status assigned to Christ in 1 Cor 15:25-28 and the probability that Paul is not likely to have violated the injunction in Dt 5:7.—If a comma is used in the same place, the reference is to Christ (so BWeiss; EBröse, NKZ 10, 1899, 645-57 et al.; NRSV text; RSV mg. S. also ε1.—Undecided: THaering.—The transposition by the Socinian scholar ET 63, ’51/52, 125f), 18b. ὁ κύριός μουκαιὰὁ θεός μου my Lord and my God! (nom. w. art.=voc.; s. beg. of this entry.—On a resurrection as proof of divinity cp. Diog. L. 8, 41, who quotes Hermippus: Pythagoras returns from a journey to Hades and appears among his followers [εσέρχεσθαι ἰεςἰ τηὰνἐκκλησίαν], and they consider him θεόν τινα) J 20:28 (on the combination of κύριος and θεός s. 3c below). Tit 2:13 (μέγας θ.). Hb 1:8, 9 (in a quot. fr. Ps 44:7, 8). S. TGlasson, NTS 12, ’66, 270-72. Jd 5 P72. But above all Ignatius calls Christ θεός in many pass.: θεοὰς Ἰ ῦ ησος Χριστός ITr 7:1; Χριστοὰς θεός ISm 10:1. ὁ θεοὰς ἡ ῶμ ν IEph ins; 15:3; 18:2; IRo ins (twice); 3:3; IPol 8:3; τοὰπάθος τοῦ θεοῦ μου IRo 6:3. ἐνα ματι ἵ θεοῦ IEph 1:1. ἐν σαρκιὰγενόμενος θεός 7:2. θεοὰς ἀνθρωπίνως φανερούμενος19:3. θεοὰς ὁ ο τως ὕὑᾶμς σοφίσας ISm 1:1.—Hdb. exc. 193f; MRackl, Die Christologied. hl. Ign. v. Ant. 1914. ὁ θεός μου ΧριστεὰἸ ῦ ησο AcPl Ha 3, 10; Χριστοὰς Ἰ ῦ ησο ς ὁθ[εός] 6, 24; cp. ln. 34 (also cp. Just., A I, 63, 15, D. 63, 5 al.; Tat. 13, 3; Ath. 24, 1;