1
to make someone cry;to move someone to tears
See also:
泣かす (なかす)
あなたが何を言っても彼女を泣かせることになるだろう。
Whatever you say will set her off crying.
2
to let cry
たまには赤ちゃんを泣かせておくのもいい。
It's OK to leave the baby to cry on occasion.
3
to grieve