I did a poor job of applying silicone sealant to the seam between a glass mirror and the splash back below it. I need to clean-up the smears that I got onto the mirror and the splash-back. How do I do this?
Wait until it dries and use a razor blade to scrape it off.
On the mirror specifically, you may be able to use acetone solvent, however this may harm the splashback. If you have extra you can test, but it will not harm glass
My go-to solvent for cleaning ANYTHING off of glass is non-chlorinated automotive brake cleaner, which is usually a mix of acetone, methanol, toluene, heptane, and hexane. HOWEVER, this is quite toxic, and will melt most rubber gloves, so you would need to take precautions in an enclosed environment (I use a multigas respirator and double up on gloves). It is also extremely flammable, If you have safer options that work, do that first.
Silicone residue can also sometimes be removed by light friction, like rubbing your finger over it with pressure, since it does not adhere well to smooth glass.
Contractor's solvent (a product similar to Goo Gone, but a different formula) does dried silicone on glass, but I wouldn't risk it on the backsplash. I would use a razor blade scraper (carefully) there. The best time to clean up silicone smears is during application, before it is set. A lightly damp sponge works okay, though if you're doing a lot of caulking you may need to rinse it often.