Depends on the grass. If it's Bermuda, for example, the stolons will permeate the bed, and eventually surface. You'll have a Bermuda bed, with some veggies trying to grow on top. In fact, if it's Bermuda, you not only have to remove the sod on the surface, but you'd better dig it up as well to get the stolons out. As a lawn grass, Bermuda is pretty indestructable. That can be either good or bad, depending on what you're trying to do.

If other thanBbermuda and you don't want to strip off the sod (best approach) a common recommendation is to lay down several layers of cardboard and set the frame on top of it, then fill. The cardboard retards drainage a bit at first but decomposes over time (how long depends on climate but 1-2 years average) and by then most grasses will have died off. Plus the presence of the cardboard decomposing helps soften the soil underneath it.

Dave

And if you don't have enuff cardboard you can use several (as in more than 3) layers (pages) of newspapers,

Also the best time to do this would be in the fall but certainly if that is not possible go for it.

The cardboard idea is a good one, and it occurs to me that with Bermuda even, a layer that doesn't decompose for a few years could well make it bite the dust. Maybe some fabric as well? Sorry to keep bringing up Bermuda, but I have a lot of it and, with regard to gardening, it gives me bad dreams.

Bermuda is a beast no doubt.

IF it were mine I would prefer something that will decompose (cardboard or newspaper) and feed the soil rather than the weed fabric which will get ripped to pieces by roots growing thru it and remain in the soil longer then we will be on this planet.

Yeah, that's probably right. Maybe enough layers of cardboard to act as a barrier for a few years, rather than just one?