Sod is a loose term. It can mean grass or 'sod'. Your other post indicates that it's grass. I have no experience with sod cutters, so you may want to look into them first. If they're not designed to actually cut nice, square strips of sod, then instead of wasting money trying to save that grass, buying new sod or grass seeds might be the better option. 
 
If you tried to cut it out by hand and replace it afterward, I doubt you'd get a nice flat (sloped) surface. It'd likely end up pretty lumpy. 
 
If it's in a low traffic area (and if you have no dogs), grass seeds are pretty easy to grow. It'll be filled right in in a couple/3 months with meticulous watering. New sod is more expensive, but all it takes is a couple weeks of watering instead of the 2 months of watering that seeds need. 
 
I know I didn't answer your question about salvaging existing sod. I'm just looking past it because I've done enough concrete work to know that old sod is rarely salvageable.
		 
		
		
		
		
		
		
		
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