I wouldn't recommend a reciprocating saw for this task. I also don't know that I'd cut along the studs personally, as that's where all the fasteners will be. Unless you have a dislike of your blade, saw motor, and limbs.

Set your circular blade depth to just less than the plywood's thickness (to avoid hitting electrical or plumbing). I'd have the electricity and water off just in case. Cut on either side of the studs they're fastened to, and anywhere else you want the sheet to come apart (for disposal). Wearing a mask would be a great idea.

Should come right down.

 

How about pull the nails. :whistling2:

 

They're pretty well recessed or covered in gobs of adhesive. But I'll take a look.

 

Claw-footed prybar would dig them out nicely.

 

A catspaw tool will get them out.