My maternal grandparents were Germans who grew up in German-speaking communities of Russia, hence their dialect might vary substantially from German as it is spoken in Germany. My mom one day recently referred to our dog as 'schnap-shnoot' (a phonetic rendition), which she translated as 'smart-nose.' But I can't find anything about it on any German language translation sites. It sounds vaguely Yiddish to me, but I couldn't find anything like it on Yiddish sites either. Is this even a real phrase? Or could it be some kind of English hybrid?
That's most likely German:
Your mom literally called the dog a "snappy snout".
"schnappen" is very straightforward - "to snap" in the sense of "biting", "grabbing" or "nipping".
"Schnut" is a dialect version of "Schnute - a term with meaning of "snout". It's a version used in the Danube Swabian dialect and this has a lot of similarities to Russian German as spoken in the small, isolated communities. Considering the context, I'm sure that is the case here as well.
If your mother gives a slightly different translation, remember that words always carry an abstract meaning and a dog that is quick to snap at something, can in English be called a "smart ...".