When the subway train __ , I wasn't clutching a grab handle, so I almost fell to the floor.
What's the verb to describe a train/subway train "taking off"?
depart is probably the best word to describe a train leaving a station, but in this context you are probably more interested in the fact that the train started moving, because this is more important to the story (which is about nearly falling over) than the fact that the train was leaving a station.
Simply holding would be better in this context.
A train pulls away from the station.