If you pray to St Cyril of Alexandria who is a Doctor of the Church, you pray to a Miaphysite saint.
If Monophysites teach that Christ’s humanity was swallowed by his divinity like a drop of vinegar in the water, Severus of Antioch is not a Monophysite:
“Flesh does not renounce its existence as flesh, even if it has become God’s flesh, nor has the Word departed from his nature, even if he has been hypostatically united to flesh which possesses a rational and intelligent soul: but the difference also is preserved, and the propriety in the form of natural characteristics of the natures of which Emmanuel consists, since
the flesh was not converted into the nature of the Word, nor was the Word changed into flesh.” - St Severus of Antioch, Letter 1
Severus does not teach confusion of the natures:
“Those therefore who confess one incarnate nature of God the Word,
and do not confuse the elements of which he consists, recognise also the propriety of those that were joined in union (and a property is that which exists in the form of a manifestation of natural differences), and not that we should ascribe the acts of the manhood only to the human nature, and impute again those of the Godhead separately to God the Word, but they recognise the difference only, not admitting a division: for the principle of union does not admit of division.” - St Severus of Antioch, Letter 1
If Monophysites teach that Christ’s humanity and divinity was mixed or mingled into one nature, Severus of Antioch is not a Monophysite
“
He did not take the flesh into the fulness of his own divine nature and mix it with it, nor did he mingle it with his own Godhead, but that in the dispensatory assumption we might understand him to be not without flesh, Emmanuel being wonderfully composed and consisting of two elements, the Godhead and the manhood: but even so
he preserved the absence, of mixture in the divine essence, and did not change the essence of the Godhead into the nature of flesh.” - St Severus of Antioch, Letter 25
Of course, Severus was an ardent follower of St Cyril of Alexandria’s Christology:
“Wherefore, we say that the two natures were united, from which there is the one and only Son and Lord, Jesus Christ, as we accept in our thoughts; but after the union, since the distinction into two is done away with,
we believe that there is one physis [nature] of the Son, as one, however, one who became man and was made flesh. But if being God the Word he is said to be incarnate and to be made man, let the suspicion of a change be cast somewhere far away, for he has remained what he was, and let the entirely unconfused union be confessed on our part.” - St Cyril of Alexandria, Letter 40:14
Hermias: But if we say that the
Nature of the Son is One, even though He be conceived of as Incarnate, all need is there to confess that confusion and commixture take place the nature of man being lost as it were within Him. For what is the nature of man unto the excellency of Godhead?
Cyril: In highest degree, my friend, is
he an idle talker who says that confusion and commixture have place, if one Nature of the Son Incarnate and made man, is confessed by us: for one will not be able to make proof thereof by needful and true deductions. But if they set their own. will as a law to us, they devised a counsel which they cannot establish, for we must give heed, not to them but to the God-inspired Scripture… - St Cyril of Alexandria, That Christ is One