How can I remove / replace this OSB floor?
You can make your cuts about anywhere, but I'd avoid leaving thin strips from the edges of the existing sheets. Some tips:


Set your saw to depth by placing it on the edge of a new sheet and lowering the table until the blade protrudes 1/8" below the bottom of the sheet. 
Consider cutting your replacement sheets first, then tracing them. This lets you cut for a perfect fit. 
Cut down the centers of joists where you can to avoid needing to add backing below. 
Cut between joists and across the joist bays where necessary. This generally isn't a problem. 
Make extra cuts as needed to make removal easier. 
Don't cut off the sheet you're standing on.


When you pull out the pieces to be removed you'll likely have strands of the sheets left behind, along with construction adhesive. Depending on how old and hard it all is, you'll need to either scrape or grind it away to bare joist. Lumps here will result in lumps later. A few gouges in the joists aren't a problem. A hammer and chisel can work well, as can a belt sander with a coarse-grit belt. 

When you install the new sheets, use a 1/4" bead of construction adhesive at all points of contact. 2-1/2" gold screws work well. Place two-by backing under all floating joints, gluing and screwing as needed. You can't really overdo this step. 

If you see any surface height issues, pull things apart and resolve them now. You don't want to have to do any sanding or grinding later. If you prepare carefully everything should remain nice and flat.