You can get little corner brackets specifically for mirrors that you can screw into the tiles. They are for flat mirrors with no frames. You can get them in Woodies/B&Q/Homebase or any DIY store.
[broken link removed]out - but they come in all kinds of metal to suit your bathroom look/feel requirements.
I don't know about sticking them on though. Adhesion to tiles will not be the best, and steam and water etc are likely to have an adverse effect on the "stickiness" of whatever you use.