According to the Catholic Church, no saint ever performs a miracle him- or herself. All miracles ever, past, present, and future, are performed by God, as the Master of His creation. In Catholic theology, saints are powerful intercessors before the throne of God conveying our prayers and supplications to Him, much like Abraham pleaded for God to spare Sodom from (deserved) destruction.
And what about those people who seem to perform miracles while alive --- and hence, by definition, not yet considered saints proper? Catholic theology would say that even in this case God is really performing the miracle (through a special indwelling of the Holy Spirit in the intermediary person), and that for some reason --- the growth of the Church, the shining of God's Glory, a sign of God's favor towards a particular teaching preached by the intermediary, the display of faith by one of His followers --- God has chosen to act through said person.
It is surprising that the Author of the universe should choose to act through mere humans --- or mere matter, for that matter. But this is the way God has revealed Himself to be and to act in the Bible.
As to your question. First of all, I should mention that I don't believe that the Catholic Church has decidedly taught whether his walking on water can be a miracle attributed to Peter specifically or not. Therefore the question is one which allows speculation and argument, with evidence proposed on all sides.
My own personal interpretation of the passage in Matthew 14 --- which interpretation I think I can defend --- is that Jesus Christ chose to reward the faith that Peter displayed on Jesus's powers when he said that Jesus could make him walk on water; the way Jesus rewarded this faith was by actually allowing Peter to walk on water --- and thus showed Peter and the other Apostles that Jesus was indeed a being whom the natural world obeyed (i.e. God).
So, the miracle of Peter walking on water gets firmly attributed to Jesus first and foremost. But how much of it can be attributed to Peter's intersession? It is, after all, Peter who asked for the miracle from God. Had Peter not asked, would Jesus have granted it? Insofar as the asking was what provided he opportunity for Jesus to act, I suppose you could say that it would not have happened without his intercession.
And yet, I do not get a sense from this passage that it was specifically the fact that it was Peter that asked that made Jesus respond with the miracle. The rest of the Gospels are full of occasions where petitioners (many of whom are not Peter) asking Jesus for miracles with great faith on His power to grant them. If one of these people had shown the faith that Peter showed when he asked for the miracle, I get the impression that Jesus would also have granted the miracle --- to reward the faith implicit in the request. In fact, when Peter's faith in Jesus' word to 'come' fails him, he starts to sink. Thus, the miracle seems to be strongly linked to the faith of Peter's belief that Jesus can deliver, more so than to his personal request, or any particular gift imparted to him by the Holy Spirit. Given these considerations, I am more inclined to give the credit of the miracle to Jesus than to the request by (specifically) Peter.
This does not deny that Peter walking on water was a powerful work. But I think this one should be attributed to Jesus instead of Peter. After all, the healing of the woman with the flow of blood in Luke 8 is not a miracle attributed to her, but to Jesus alone! On the other hand, the healing of the lame man on Acts 3:6 would definitely be a miracle attributed to Peter. What is the difference? There seems to be a greater amount of agency by Peter in Acts 3 than in Matthew 14. In Acts 3 Peter attempts to heal the lame man himself, using the power of God (which power God does give in this instance). In Matthew 14 it is Jesus who acts to bring about the miraculous, not Peter.