When I first went to night school to have my first computer lesson, the instructor told us that one good rule to remember is never take food or drink anywhere near a computer.. But I would guess we all do so at some time or other because like you I am having a coffee right now too. I would just put the mouse mat in a bowl of washing up water and let it soak for a while then rinse it a few times and dry it in an airing cupboard or out in the sunshine on a flat surface. ..Bingalau..
Get a bowl of hot water with a LITTLE washing up liquid in it. Thoroughly wash the mat and stick in airing cupboard overnight. It will be fine. If you use a n optical mouse you do not need a mat so I assume you are using a rollerball mouse.
I have an optical mouse but still use a mouse mat. I cover it with a sheet of A4 paper as all the mouse mats I own have some form of dark patterns or wording on, which can cause problems for the mouse's efficiency.