I had a Lubavitcher classmate in high school who used to spill off from his cup whenever he would drink anything. He claimed it was a minhag.
What is the reason/source for this practice?
It's from the Gemara, Chullin 105b (bottom):
ואמר אביי: מריש הוה אמינא האי דשדי מיא מפומא דחצבא - משום ציבתא; אמר לי מר, משום דאיכא מים הרעים
"Abaye says: I used to think that the reason people pour out some water from the lip of a pitcher [before drinking from it] is because of floating bits [Rashi: twigs and straw that are floating on the water]; but my teacher [Rabbah] told me that it's because of 'evil waters' [Rashi: a shed (demon) may have drunk from it, and this corrects the problem]."