Throw a couple of sheets of newsprint over the grass, then toss the new soil over the paper.

I agree with Alex. I built, ahem..my DH built an herb garden and before we filled it with dirt, we put about 10 layers of newspaper down to keep the grass out. The garden is on the side of the house, so the only grass we had was the stuff that was creeping under the edging and popping up in the bed. I didn't want to have to deal with the chance of grass in my herb garden, so we put paper down.

What kind of grass is it?
We have the sodded bermuda and my neighbors said it came up in their beds. But I dumped 4" of dirt on it and planted and so far no problems and I have a lot of beds. The stuff barely grows without fertilizer so I don't see how it wouldn't be easily smothered if that's what you got.

I think most of the grass is Centipede but I'm not sure and there are some weedy grasses in it, too. I think I will try using the newspaper down first, then fill with the soil. Removing the sod is REALLY hard work.

I agree with Alex & efam too. The newspaper trick works great, it eventually disintegrates and it doesn't take too much time to do. Broken down cardboard boxes work well too, just takes a little longer to disintegrate. I used these on a tough, weedy island with lots of thorny underground vines last year and didn't even spray the weeds first. It's been nearly a year and those buggers haven't poked their heads up once so I think it's done a good job in smothering them and blocking the sun.

Squirrellypete