Some products have that notorious holosticker on them "warrnty void if removed". Macs don't have that (except on some of their processors) so you can replace the memory if you like. Now if you damage something, they won't cover what you damaged, but that's to be expected. It's possible for a user to replace memory in a mini but you really need to go to one of the web sites that shows you how to do it, so you don't break something or cause more than minor cosmetic damage. (it's really not possible to open a mini without marring the bottom plastic lip a tad bit so don't feel bad if you can tell it was opened after you're done)

You'll want to obtain a small putty knife, the kind with a blad about 5" long and about 1.25" wide. If you have a choice, get one with the thinnest possible blade. It helps tremendously to file the edge of the blade on one of its flats to make the end edge sharp like a knife, which can be achieved by rubbing it at a generous angle on concrete for awhile. Once you have one end cracked open 1/4 inch or so, stuff a credit card in and remove the blade, and work the other end. If you don't put something in the opened end, it will close when you try to insert the blade on the other end.

Pay attentopn to the length of the screws you remove, some are longer than others and they need to go back where they belong.

Depending on your mini, there may be 1 or 2 two-wire cables to unplug. If you are going to break something, this is likely it. Be careful not to pull the wires out of the jack, or to pull the plug off the board with the jack. Most tutorials talk about caution with the ribbon cable bail, and that IS fragile too, but people usually exercise more caution with it so it's actually less likely to be damaged during disassembly. If necessary, use a very small flathead screwdriver to help separate the jack from the plug by inserting the screwdriver tip into the join between the two and twisting (not prying) it.

You can test the mini during reassembly before replacing the outer shell. I recommend this. You need to make sure the sleep/power light and the power button work, in addition to just plain booting up.

There are many guides on doing this and a few videos of opening the case also. Links like this come and go so you may have to search for a fresh link but here are a few that worked for googling on "upgrade memory mac mini video"

http://www.methodshop.com/2006/07/mac-mini-ram-upgrade-tutorial.shtml
http://www.youtube.com/watch?v=8xKlRWw89jI