My approach would be to sit crouched with my head in the joist bay, mark a line with a speed square, and cut most of it with a battery circular saw. You could clamp the speed square to the joist as a saw guide with the appropriate offset, if desired.
Then to finish the cut, take your pick: hand saw, reciprocating saw, jigsaw (which won't quite finish but will get closer than the circular saw, usually), oscillating saw.
If you're remodeling and have several cuts to do in one area, it's worth considering pulling up an area of subfloor so you can easily do the whole cut with a circular saw.
Cheers, Wayne