Re: Looking for the name of a technique
It sounds like you're describing a variation of what would be men-uchiotoshi-men in kendo terminology. When done correctly it is a very effective technique, but it is difficult to do correctly, and is thus a high level technique. If all you do is tap, then you're not going to break your opponent's kamae, and you should expect to get cut in side of the abdomen when you swing up--Your side will be much closer to your opponent's sword than his head is to yours. However, if you cut down his attack just before it would come to stop, which requires very precise timing, from the correct position, which requires very precise control of maai, then your opponent's sword will be put far out of position, and they will have their weight forced onto their forward leg, temporarily planting them in place, giving you plenty of time to cut them.
At the very high levels, the uchiotoshi and cutting the opponent become one and the same, making a one-beat technique in which you cut through their attack to the target of your choice.