We are traveling to the Mexico. If I buy something in Mexico, can I ship it home by UPS or mail. The last time I cruised I carried a heavy piece home, and I think it might be easier to ship it.

The short answer is yes, you can. In fact it's probably a good idea. Most reputable stores will even handle all the details for you. If it's your first trip to Mexico it's probably best to stick to stores recommended by your ship (o.k., we all know they get kickbacks, but you have to start somewhere!) And pay by credit card; you may lose a little in the exchange rate but at least you have a good record of the transaction.
In exchange for my valuable information, you must now tell me where you are going and on what ship.

I am cruising on the Carnival Pride in April. I think that our excursions will be Ziplines & "spa time" in PV. Shopping, old town in Mazatlan, maybe a booze cruise for the 20 year olds, and lying about in Cabo....I am really looking forward to it. I would like to buy some stained glass or pottery, but it is so large and bulking, I think that it might be easier to ship it if I could. Just a thought.

Sounds like a GREAT trip!
I've always wanted to try ziplines--maybe someday I'll get up the nerve. Mazatlan is definitely the place to do your shopping. I have not seen a lot of stained glass, but pottery is abundant; and shipping it home is the thing to do.
Haven't been on Carnival Pride but I've read a lot of good things on this site.
Have a great trip and let us know how it went.