If you're in less of a hurry, and starting in the fall, you can use a layer of newspaper under a layer mulch to kill the grass. Works well here in zone 8 with warmish and wet winters, not sure how it would work in colder and drier areas. I imagine it would still kill the grass, but wouldn't decompose as quickly, so you might have to pull a bunch of paper out when you till it up in the spring.
Sod cutter if you've got enough space to work it, but my experience in tight spots in my yard is the only tool to use is a pulaski. Hard work, but gets at the grass roots better than a spade.
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