Dear Dwight
No one in the Bible has ever taught that God has blood. Why would you think that God has blood?
Over and over, the Bible (including Paul in numerous instances) refers to the blood of Jesus, not to the blood of God.
What happens in this passage, then? A copy error or translation error. Just that.
"His own" should have been translated by "his own Son", to be compatible with all other Scriptures.
That's why several translations now yield the verse differently:
Watch yourselves and the whole flock, in which the Holy Spirit has placed you as supervisors, to shepherd God’s church, which he obtained with the death of his own Son. (CEB)
“Watch out for yourselves, and for all the flock in which the Ruach HaKodesh has placed you as leaders, to shepherd God’s Messianic community, which he won for himself at the cost of his own Son’s blood. (CJB)
Be on guard for yourselves and for all the flock among which the Holy Spirit has appointed you as overseers, to shepherd the church of God which he obtained through the blood of his own Son. (LEB)
Watch out for yourselves and for all the flock in which the Holy Spirit · has placed you overseers, to shepherd the church of God, which he purchased with the blood of his own Son (MOUNCE)
Be careful for yourselves and for all the people the Holy Spirit has given to you to oversee. You must be like shepherds to the church of God, which he bought with the death of his own son. (NCV)
Watch out for yourselves and for all the flock of which the Holy Spirit has made you overseers, to shepherd the church of God that he obtained with the blood of his own Son. (NET)
Keep watch over yourselves and over all the flock, of which the Holy Spirit has made you overseers, to shepherd the church of God that he obtained with the blood of his own Son. (NRVSA)
Take heed to yourselves and to all the flock, in which the Holy Spirit has made you overseers, to care for the church of God which he obtained with the blood of his own Son. (RSV)