If your basement is unfinished, you should have an easy time with it. I would suggest, though, rather than cutting from the center of one joist to the center of another, that you cut inside to inside - then, from the basement side, screw in a 2x piece of material on the inside of each joist at your hole to give you a full inch and a half support at the ends of your new subfloor patch ... when you've only got 3/4 inch overlap, minus 1/8 tolerance, that's only 5/8 and with some concentrated weight that short span can sag enough to pull free from one side or the other. It's not very likely, but still possible. A wood finished floor would add some structural stability, but vinyl's tiles will remain flexible.