Should τῷ πνεύματι αὐτοῦ in Mark 8:12 be translated as meaning "with his breath?"

Question

Deeply sighing ἀναστενάξας involves one's breath. The word πνεῦμα has the meanings breath and wind, as well as spirit. Translating τῷ πνεύματι αὐτοῦ as "in his spirit" implies that Jesus gave no visible appearance of sighing. This doesn't seem to match ἀναστενάξας, which means "deeply sighing."

In English "with his breath" is somewhat redundant with "deeply sighing." Thus, NIV1984 translates Mark 8:12:

He sighed deeply and said, “Why does this generation ask for a miraculous sign? I tell you the truth, no sign will be given to it.”

Many translations translate τῷ πνεύματι αὐτοῦ "in his spirit."

Appendix

Note ר֥וּחַ in Hebrew means the same thing as πνεῦμα in Greek. Here it means breath.

בִּדְבַ֣ר יְ֭הוָה שָׁמַ֣יִם נַעֲשׂ֑וּ וּבְר֥וּחַ פִּ֝֗יו כָּל־צְבָאָֽם׃ (Psalm 33:6, BHS)

       By the word of the LORD the heavens were made, 
 and by the breath of his mouth all their host. (Psalm 33:6, ESV)

Answer 1

There are two possible ways to understand the phrase of Mark 8:12 - καὶ ἀναστενάξας τῷ πνεύματι αὐτοῦ (= and having sighed deeply in the spirit of him) -

1. As a classical redundant Hebraism. The NT is full of such redundant Hebraisms such as V28, "and they answered him say ..." see also Matt 23:1-2, 28:18, Luke 14:3, 24:6-7, etc. Mark 7:25 has another, "A woman whose little daughter of her had an unclean spirit."
2. BDAG has 8 basic means for the word "pneuma". BDAG #3c has "spiritual state of mind, disposition" (eg, 1 Cor 4:21, Gal 6:1, Eph 4:23, 1 Peter 3:4). IF this is understood as the meaning here, the the phrase above might be idiomatically translated. "and having sighed deeply in his mind" = "internally groaned" or similar.

Either of these is consistent with the idiom of Scripture. I personally prefer the first without excluding the second. The NIV allows for either as well.

Barnes notes:

Sighed deeply in his spirit - His heart was deeply affected at their wickedness and hypocrisy. The word "spirit" here is taken as the seat of the emotions, passions, affections. He drew groans deeply from his breast.

The Jamieson-Fausset-Brown Bible Commentary has something similar:

12. And he sighed deeply in his spirit—The language is very strong. These glimpses into the interior of the Redeemer's heart, in which our Evangelist abounds, are more precious than rubies. The state of the Pharisaic heart, which prompted this desire for a fresh sign, went to His very soul.

Gill also appears to support the second meaning above:

And he sighed deeply in his Spirit,.... In his human soul; and which shows that he had one, and was subject to grief and sorrow, and all passions and infirmities, excepting sin. This deep sigh was on account of the hardness of their hearts, the malignity of their minds, and insincerity of their intentions; who had no view to come at truth by this inquiry, but to ensnare him:

Answer 2

There is an interesting parallel in John where a similar word is used. ἐμβριμάομαι is used of the snorting of a horse, but also a heavy and deep sigh.

ἐνεβριμήσατο τῷ πνεύματι (John 8:33)

Ἰησοῦς οὖν πάλιν ἐμβριμώμενος ἐν ἑαυτῷ (Joh 8:38)

In the first one Jesus sighed deeply in spirit and in the second he sighed deeply in himself. The reason for the deep sighing in spirit is in both contexts the unbelief of the people around him. I would therefore prefer to keep the spirit both in Mark 8:12 and John 11:33. The sigh (deep breath through the nose) could probably be heard, but the spiritual frustration could not be heard, so it is made explicit by the authors.