You are basically asking us if the (articulated form of the Greek word for) God from the end of one chapter is basically a throwback to an expression used at the beginning of the previous chapter. At first glance, this might seem somewhat unlikely, but, in all fairness, I think you meant to ask two questions at once, only to end up being detrimentally parsimonious to oneself; thus, allow me first to rephrase your own question, so that it might make more sense, both to myself, and other readers:
- Is the article at Titus 2:13 ultimately anaphoric to θεός at Titus 1:1-4 ?
Or, to unpack it even further:
Is the expression at Titus 2:13 a throwback to the one mentioned just verses earlier, at Titus 2:10-11 ?
Does the expression at Titus 2:10 reference the same entity as the similar one employed previously at Titus 1:3, and, later on, at Titus 3:4 ?
Are the articles at Titus 1:2-3 anaphoric to the two unarticulated forms found in the previous verse ?
To state matters plainly, you seem to have the following hermeneutic approach in mind:
Titus 1:3 But hath in due times manifested his word through preaching, which is committed unto me according to the commandment of God our Saviour.
Titus 2:10 Not purloining, but shewing all good fidelity; that they may adorn the doctrine of God our Saviour in all things.
Titus 3:4 But after that the kindness and love of God our Saviour toward man appeared...
with a possible (and arguably plausible) interpretative key provided by:
Titus 1:4 To Titus, mine own son after the common faith: Grace, mercy, and peace, from God the Father and the Lord Jesus Christ our Saviour.
Note: The following sentence is neither an argument used in the OP, nor a grammatical observation. The OP is entirely grammar. End Note.
along with the observation that whenever the word God appears in the vicinity of Christ, it usually refers to the Father:
Titus 1:1 ¶Paul, a servant of God, and an apostle of Jesus Christ, according to the faith of God's elect, and the acknowledging of the truth which is after godliness.
Titus 1:4 To Titus, mine own son after the common faith: Grace, mercy, and peace, from God the Father and the Lord Jesus Christ our Saviour.
thus substantiating the proposed interpretation of:
Titus 2:13 Looking for that blessed hope, and the glorious appearing of the great God and our Saviour Jesus Christ.
as referring to two distinct entities, rather than one. Though not impossible, let us also take a closer look at the way in which the word Savior is employed throughout the Epistle:
Titus 1:3 But hath in due times manifested his word through preaching, which is committed unto me according to the commandment of God our Saviour.
Titus 1:4 To Titus, mine own son after the common faith: Grace, mercy, and peace, from God the Father and the Lord Jesus Christ our Saviour.
Titus 2:10 Not purloining, but shewing all good fidelity; that they may adorn the doctrine of God our Saviour in all things.
Titus 2:13 Looking for that blessed hope, and the glorious appearing of the great God and our Saviour Jesus Christ.
Titus 3:4 But after that the kindness and love of God our Saviour toward man appeared...
Titus 3:6 Which he shed on us abundantly through Jesus Christ our Saviour.
Note: The previous examples of "Savior" don't employ a grammatical analysis and are merely comments on superficial similarities in the English text. If it is meant as applicable to the OP, that needs to be fixed. These phrases are discussed in the original paper (See Titus 3:6) and applied with Greek grammar. That would be a good starting point. End Note.
The rhetorical mechanism employed here seems thus similar to the one used in the Prologue to John's Gospel, as well as 10:28-29, wherein the various attributes of God are portrayed as being mirrored in Christ; as such, it would not be farfetched to interpret the somewhat ambiguous expression of 2:13 (the great God and our Saviour Jesus Christ) as a combination of the other two (namely, God our Saviour and Jesus Christ our Saviour).
Note: Neither alleged "rhetoric mechanisms" or rhetoric nonsense are grammatical arguments. This should be excised from this answer. End Note.
Therefore, in conclusion:
Is the article at Titus 2:13 anaphoric?
It might be.
(And please stop formulating your questions in such absolute language; i.e., don't ask whether it is, but rather whether it could be, or, alternately, to what extent it would be plausible to regard it as such).
If so, what is its antecedent?
The similar phrase just three verses earlier, as already stated above.