Within that sentence are two statements. The first is that the Father (who is the vine-dresser) will take away the branch that does not bear fruit. The second is that the Father will prune the branch that does bear fruit so that it may bear more fruit.
If this parable was the only place in the New Testament to address the issue of eternal security, then there would be every reason to fear that a lack of “fruit” would result in the loss of salvation. But it isn’t. Please read John 6:39-40:
“And this is the will of him who sent me that I should lose nothing of all that he has given me, but raise it up on the last day. For this is the will of my Father, that everyone who looks on the Son and believes in him should have eternal life, and I will raise him up on the last day.”
Given that John 15 is a metaphor or an allegory, then we do well to consider it in the light of other passages that speak clearly about the assurance of salvation given to those who have come to saving faith in Christ Jesus. It would be foolish to take three verses alone to support a view, one way or the other.
Isaiah 5:1-7 is a striking Old Testament image of Israel being likened to an unproductive vineyard that is rejected by God and made into a wasteland. Here, God is rejecting his people because they have rejected his law. No doubt, Jesus’ audience were familiar with the illustration. But God has never entirely abandoned his people, and even in the future, all of Israel will be reconciled to God. Yes, there is a dire warning against any person who claims to belong to God yet proves by their actions (or lack of actions) they have only an outward profession of faith.
In Matthew 13 Jesus gave a parable about seed that fell into different types of soil. Some plants start to grow but then wither away. Does that mean the person who has been adopted into God's family has no security, that they must constantly strive to do good works? No. If a branch is not receiving the life-giving nourishment it needs from the roots, then it will not produce fruit. If a person is not genuinely abiding in Christ and living their life to the glory of God but is simply pretending to be a Christian, then they too will wither away like the seed that fell onto stony ground. Jesus will say to them, “I never knew you.” If a person does not obey Jesus then they are not a part of the one, true vine.
You ask, does John 15:2 disprove “once saved always saved?” Frankly, that expression is so misleading I reject it because it gives entirely the wrong idea about the grace of God and the doctrine of salvation. I put it to you that John 15:2 neither proves nor disproves any false assumption that a person can make a claim to be a Christian without producing evidence of a transformed life, a life that produces the fruit of the Spirit. Only those who are indwelt by the Spirit will mature and grow in their Christian walk, producing the fruit that brings honour to our Lord and Saviour. All I can say is it’s a good job Jesus knows who belong to him.