There are many verbs that sound like tatsu/tachimasu, and they all have different meanings. Just a few of them:
立つ - to stand
経つ - to pass (as in, time passes)
建つ - to be built (as in, a building is erected)
断つ - to cut off all ties with someone (or also, literally/physically cut something off)
deru (出る) means simply "to go out"/"to leave a room", so not quite as dramatic as 断つ.
There are still more ways of expressing "leaving" such as 放っておく (hotte oku) and 去る (saru), each with their own nuances.