"Maman t'appelle, vas-y !"
Translation:Mom is calling you, go!
Yes. aller - to go - requires a destination (or implication of one).
Je vais au marché → I go to the market
J'y vais → I go (there)
Well, some of "us" do and others of "us" don't. Brits use "mum" a lot, even for HRH the queen. In the States, it's generally "mom", not "mum". Both are accepted.
"Mom is calling you go" is improper English. The word "to" should have been offered.
"Go!" is in the imperative as a translation for "vas-y !", which is also in imperative. You just need a comma after "you" to make the sentence relevant and correct.