You can use this phrase when someone leaves a company, graduates from a school, etc. You can say this about someone:

I'm sorry to see her go.

Or you can say it directly to someone:

Well, I'm really sorry to see you go.

You can also use this phrase when someone dies. It's a little bit too casual to use when you're speaking to the dead person's family or close friends. But if you're talking about someone who neither you nor the listener was very close to, like a neighbor or a celebrity, you can say something like:

He seemed like a nice guy. I'm sorry to see him go.

This phrase also wouldn't be strong enough to use when talking about something like breaking up with a spouse or lover.