Help with floor rot removal, picture included

https://www.amazon.com/WEN-2312-Variable-Multifunction-Oscillating/dp/B005UKGKYK

A occillating tool will work the best for
Cutting near the edges. Had same problem in my MH. Styro is cheap. I would do it all and do it right. What's under the styro? I would take a look.

If you have a glass shop around you that does windshields. There is a putty type knife that fits in the end of a reciprocating saw. You should be able to use it to just shear the plywood off.

I would advise completely coating the under carrage of the unit. This is where most of your rot starts.

If the adhesive bond still exists between decking and foam, you may have to cut the wood in smallish pieces and then horizontally shear the wood from the foam. You may still have some foam stuck to any solid wood removed or may have wood bits still stuck onto the foam. The alternative is to cut it all out and build another composite.

Your picture shows a typical neophyte process, picking at the vinyl and wood for removal around the discolored decking. I'd suggest to establish a square area border beyond the discoloration, remove the vinyl and proceed.

Another typical assumption is that all that discolored wood needs to be removed. It does not. Any wood that has failed glue bond to foam needs replacement or adhesive injected underneath to reestablish the bond. The discolored wood can be treated with bleach/mildicide and epoxy to make any mold inert.

you likely aren't going to get away without taking out the foam. Actually, the foams integrity is likely been compromise by the moisture anyways. You best best is to replace the foam with sheet "foam" insulation using in building / homes.