Something which is described as 'tearing your heart out' is extremely upsetting or distressing. This is a very emotive phrase used more in informal contexts to express concern, empathy or emotion.

1. The sight of those starving children is enough to tear your heart out. I wish I could do something to help them.
2. You need to stop treating Janet this way. Can't you see that you're tearing her heart out?
3. Hearing what that man had to go through tore my heart out. I just burst out crying.

1. The footage of people's homes being destroyed in the floods would tear your heart out. We need to find out how we, as a company, can help.
2. That client would tear your heart out.  He's never happy and always wants to change things at the last stage.