No, we are not Monophysite at all and have never been.
Monophysites is an idea that the humanity of Christ is swallowed up in his divinity is an error that has never been accepted. Those who teach that in Jesus Christ there is not a duality of perfect humanity and perfect divinity in unity, but a single mode of being which is either the divine only, so that he is not properly human at all, or some new mode of being, so that he is neither one thing nor another but something different from divinity and humanity. The idea that Christ is of some new mode of being that is a mixture of humanity and divinity is an error that has never been accepted. Therefore the belief of ‘Monophysites’ “called Eutychianism” is who believe in One Single Nature (Divine) of our Lord Jesus Christ.
The Oriental Orthodox Churches (Coptic, Syrian, Armenian, Ethiopian, Eritrean, Indian) are ‘Miaphysites’. the ‘Miaphysites’ who believe in One United Nature or One Composite Nature (Divine & Human) of our Lord Jesus Christ. We do not believe in a Single Nature but we believe in One Incarnate Nature of the Logos. "Our Lord Jesus Christ is one, perfect in his humanity and perfect in his divinity, at once consubstantial with the Father in his divinity, and consubstantial with us in his humanity. His humanity is one with his divinity—without change, without commingling, without division and without separation". St Cyril.
In Short this is what the Oriental Orthodox confess- Our Lord Jesus Christ is one because He has one identity, He is God the Word incarnate, The Logos, while He remains always after the union of humanity and divinity both human and divine. While He is human and divine, the Son of Man and the Son of God- this does not make him two persons or identities, nor does it even make him a God and a man alongside each other joined in some way. It is the one God the Word who is perfectly human and perfectly divine in an incomprehensible unity that does not confuse or mix, separate or divide.
When we speak of Our Lord nature of union - “We speak of neither confusion nor division nor change. Anathema to whoever speaks of confusion or change or mixture”. St. Dioscorus