Choice of words referring to being attacked/assaulted with a glass/cup

This meaning of glass is not that recent. According to the Oxford English Dictionary:

trans. slang (orig. and chiefly Brit.). To strike (a person) with a (broken) glass or bottle, esp. in the face.

It was first noted in the 1930s. However, it is a transferred sense of the word--it is likely that the meaning is creating a use like "stoning" out of "glass". Therefore, it is possible that "mugging" could gain a similar transferred sense.

However, mug already has a fairly accepted usage as a verb where glass as a verb does not (at least, not in current usage). Thus, I think it is less likely for mugging to gain the same form of transferred meaning.

I don't think glassing would apply to the coined mugging, as it seems to refer more to a broken bottle. A term you might use in this situation would be that one was "stabbed with a makeshift weapon". This is clunky, but then one could describe exactly what common item was turned into a weapon.

Glassing, as in stabbing someone with a broken bottle/glass, was given its own word because of how common it was. Doing the same with a mug is hardly commonplace. As such, I'd recommend the more generic shanking which refers to the act of stabbing someone with a homemade or improvised weapon (as is commonplace in prison).