Need to fix the grading of my backyard: remove the sod or turn it over?
I have not had a good experience with tilling an existing lawn. The existing grass does not get shredded completely but will form lumps that make for an uneven surface. Depending on how much top soil you have, you may bring out a lot of sand and rocks. Even a small electric tiller can go as deep as 6-8 inches. If your top soil is not at least 12 inches, it will be a long and labor-intensive process to get back your lawn without spreading additional screened loam. 

What a landscaper will do with a bobcat (as I have just observed in my neighbor's yard) is


scrape off the sod and discard
try to salvage as much loam as possible and dump it on a pile that is out of the way
grade the land as desired
re-spread the loam, and add new loam if needed
reseed