Actually there are two meaning in "놓다" which is the base form of "놓고". As Jin said literally it means to put/place sth swh, and it is also used to mean "when sth happened, let it remained in the same state as it happened and other things happened or you did sth without caring about the previous thing". (sth = something, swh = somewhere) It can be interchangeable with "~ (한)채" For example, They went to the movies leaving me alone. 나만 빼놓고 그들은 영화 보러 갔다. = 나만 혼자 (내버려)둔 채 그들은 영화보러 갔다. Mom went out leaving the light on yesterday. 어제 엄마는 불을 껴놓고 외출했다. = 어제 엄마는 불을 껴둔 채 외출했다. = 어제 엄마는 불을 껴놓은 채 외출했다. She promised that she wouldn't leave me, but she did.(T.T) 그녀는 날 떠나지 않겠다고 약속해 놓고 날 떠나버렸다. Looking at your sentence, 그녀는 내맘을 찢어놓고 떠나버렸다. = 그녀는 내맘을 찢어놓은 채 떠나버렸다. = 그녀는 내맘을 찢어둔 채 떠나버렸다. She left me having torn/broken my heart. \^o^/

^^ it's so difficult to explain... we say it when we want to stress or emphasis status or action. The original meaning is "to put/leave/let sth". so actually 내 마음을 찢어놓고 is same as 내 마음을 찢고. (굳은 마음 적셔놓고= 굳은 마음 적시고) But 적셔놓고 or 찢어놓고 is stronger ....