My father in law, just used a sod cutter 2 weeks ago or so. He had to move his grass to level it with a new patio that got installed.

Anyways, the spots of his that he had dead grass, cut and pulled up just like the grass cuts. The dirt Was moist, so maybe thats why it stuck together as though it had grass growing in it, it did have roots all through it though imagine that was more of why it worked than the dirt being wet.

His soil was heavy clay.

I rented a sod cutter for my dead grass and it didn't work. The cutter didn't cut into the ground at all. The depth lever shook loose as soon as it hit the ground, even though it was tightened very tightly. Total waste of time and money. I think in my case the problem was that the ground was very dry and hard. I hadn't watered the dead grass for some time, it hasn't rained and it's been a long time since the ground was deeply watered.