Does the One God Have Three Different Modes? (Modalism, Sabellianism) (blueletterbible.org)

"Modalism, or Sabellianism, is inadequate view of the nature of God. The doctrine arises from a bishop in the early church named Sabellius. Modalism teaches that only one God exists and that the three persons listed in the Bible, the Father, the Son, and the Holy Spirit are modes or manifestations of the one God. As one human being may be a father, son, and husband at the same time, yet the person is only one individual, so it is true with God the Father, God the Son, and God the Holy Spirit. There are no distinct persons within the nature of God from the modalistic point of view. It is Unitarian in that it accepts only one Person in the Godhead

Attempts To Preserve Unity

Originally the intent of Modalism was to preserve monotheism (that is the belief in the existence of the unity of the one God) while still holding to the divinity of Christ. But the Trinity of Modalism is a Trinity of manifestation. This means that the three personalities are expressions of the one person of God. The Trinity of the Bible is a Trinity of being which means the three persons are distinct persons within the nature of the one God.

God Is A Changing God

Modalism also undermines the Biblical teaching that God never changes for it portrays a God who changes His modes. The Bible pictures God as unchanging:

For I am the Lord, I do not change (Malachi 3:6).

Furthermore, Modalism takes away from the mediatorial work of Christ. The Bible teaches that Jesus is a mediator between God and humanity.

For there is one God and one mediator between God and humanity, the man Christ Jesus (1 Timothy 2:5).

The Modalistic view of God, that the Father and Son are the same person, would have God mediating between Himself. This is not biblical or logical.

The Father And Son Are Distinct

Modalism does not fit the facts The Bible says the Father loves the Son,

The Father loves the Son and has given all things into his hand (John 3:35).

Jesus said.

For the Father loves the Son and shows him all he does. Yes, to your amazement he will show him even greater things than these (John 5:20).

This does not mean the Father loves Himself.

Scripture says the Father sent the Son.

Jesus therefore said to them again, "Peace be with you; as the Father has sent me, I also send you" (John 20:21).

He did not send Himself. The Bible also says the Son returned to the Father.

Jesus said, "Do not hold on to me, for I have not yet returned to the Father. Go instead to my brothers and tell them, 'I am returning to my Father and your Father, to my God and your God'" (John 20:17).

The Son did not return to Himself.

The Father Sent The Holy Spirit
The Bible says Father sends the Holy Spirit.

But the Helper, the Holy Spirit, whom the Father will send in my name, he will teach you all things, and bring to your remembrance all that I said to you (John 14:26).

Again, He is not sending Himself.

Modalism Is Inconsistent And Confusing

If the Father, Son, and Spirit are the only God under three different names or modes, then the New Testament would be totally inconsistent and confusing. For example, in the prayer of Jesus Christ, recorded in John 17, He is addressing His Father. According to Modalism He is praying to Himself. Such an idea is absurd.

Summary

Modalism or Sabellianism is a non-biblical way of understanding the nature of God. It is one of the heresies under the heading of Unitarianism. Modalism says that there is one God who manifests Himself in three different modes. God sometimes manifests himself as the Father, at other times as the Son, and still on other occasions as the Holy Spirit. The God of Modalism is a changing God. This concept of God is opposed to what the Bible teaches. First, the Bible says that God exists in three distinct Persons - the Father, the Son, and the Holy Spirit. He is not merely one Person as the Unitarians believe. In addition, the God of the Bible does not change - his nature stays forever the same. 

Finally the Bible gives examples of Jesus praying to the Father. According to Modalism he would be praying to himself. This is a ridiculous idea. Consequently the God of Modalism is not the God of Scripture.