When I read your post, I thought of the time I put chicken wire under the grass. It was the only way to stop our Lab from digging holes to lay in when it was hot. I had to do something as a couple of times he actually dug under the slab on the house.

If it has been there for many years why do you feel it is necessary to remove it?

If it is plastic you may be able to break it up with an plug aerator.

If you want a flower bed or to plant a tree remove what is necessary and forget the rest.

I agree with knuttle, why do you want to remove it? It shouldn't really affect the lawn or taking care of it unless the netting is sticking up above the grass, but then you could just cut it off with a knife or scissors.

Why remove it? You do not til a yard.

Rototilling is for veggie gardens (which I disagree with, too) but NEVER for a lawn. Leave the mesh in place and proceed.

Where do you live (now)?
What kind of grass/weeds do you have now?
What do you want?
Are you willing to water when the grass needs it?

I've got the plastic/nylon mesh throughout my backyard. It has never been a problem doing aeration, slit seeding, or verticutting. I know of no effective way of removing it and believe me, in the beginning I tried. Although, I would certainly expect that roto-tilling would remove it. Not sure how you would remove it from the roto tiller tines. Just kidding, don't roto-till a lawn.

Folks need to quit watching TV and wannabe gardeners on PBS and other networks.