Tear down bathroom floor?

[-JC-]

I will soon tear up the existing bathroom floor with tiles. I assume the base directly on the beams is glued and screwed (I think there are tongue-and-groove boards underneath). Do you have any tips on how to tear this up in the smoothest way without damaging the beams too much? The beams run through the house, outer wall to outer wall.
I'm thinking of removing the tiles, then sawing through the rest of the floor along the beams. Then place a straightedge (board or the like), securing it along each beam as support and sawing with a jigsaw perpendicularly across. This way I can (hopefully with decent precision) remove material from the beams so I can glue and screw a strip of 12mm construction plywood and get an even base for the floor chipboard.
How have you done it?

 

[vectrex]

Self-demolition sounds reasonable, but cutting through the floor joists from the side with a jigsaw sounds incredibly complicated.

Instead, attach a 2x4 to the side of each floor joist, allowing it to stick up slightly above the old floor joist. This way, you easily get a new and even surface to screw-glue the floor particleboard into!