You have a couple of choices in Simpson Bay, as well as several other choices if you travel a bit further.

The closest large supermarket in Simpson Bay is the Market Garden. Frankly, I don't recall that I've ever purchased meat there, because I think their prices overall are very high. It is a large supermarket though, with basically anything you could want. Be advised that they do not provide plastic bags though, so you should bring some or prepare to pay for them.

In Simpson Bay proper, other than the Chinese groceries, the only other super market is the Gourmet Grand Marche. They don't have only gourmet items, they have regular items, but it's a smaller store than the regular GM's, and frankly, never purchased meat there either, as their selection isn't very large.

If you travel a bit further from Simpson Bay, you have a lot more choices. You have the Grand Marche in Cole Bay, which is a large store and carries everything, with some emphasis on French items, but they have a large selection of meats of all kinds. I personally prefer the Grand Marche by the roundabout on the way to P'burg, possibly because that's the one we have gone to for years and years. They have everything, including nice meats. You also have the Fresh Market, in Cole Bay. We haven't been there in a while, but they used to have the best produce on the island. Never bought meat there, although they do have a nice selection of everything. The BEST deals on the island right now are at the Super U, which is in Marigot on the French side. It is where the Match used to be, years ago. They have the best prices, wonderful selection, and also a lovely selection of french products. You also have Simply in Hope Estate on the French side--basically by the roundabout for French Cul de Sac. I've never purchased meat there, but it is a large, full service store. Oh, and I forgot, you have Cost U Less, by the Grand Marche at the roundabout, which is basically like a Cost Co. They have larger sizes of many items, but their meat is generally first rate. Lots of choices!!