Mulching my beds?

There are a few "piles" of grass clippings/leaves that I have discovered on our land. The top layer is partially broken down, and looks like it was added last year, before we moved in. Below that it's slightly better broken down, and a bit matted in places.

I've never mulched before, so as an afterthought, I decided to to try mulching my just dug beds before I put my veg in this year. But after doing a bit of searching/reading on the web, it seems that it may be bad for the soil - the mats stopping oxygen getting to the soil.

So my question is, now that I've done it, should I undo it?

I am planning on getting a paper shredder so I can mix the stuff with grass mowings in a compost bin.

Thanks for the replies/advice.

I forgot to mention, there is also quite a bit of moss mixed in with the grass clippings and leaves which appears to have helped stop it all getting too matted. The majority is fairly loose or in the form of hand-sized clumps.

We do have a shredder, but have been saving all our paper/card to help get our multi-fuel burner started. I think when the time comes to cut the grass I'll collect some of the leaves that are still sitting on the ground in places from last autumn and scatter them over the lawn before mowing it.

As for the slugs and snails, my idea is to surround our veg with a layer of sharp sand, so hopefully that will deter them. It's worked quite well for me in the past.