To take all of the resources that another person or thing has available. This phrase is often applied to money. Paying for my kids' education is just bleeding me dry. I hope I'll still be able to retire one day! Overhead costs are bleeding our business dry. We need to come up with a different way of doing things.

To take all of the money that another person has, often through blackmail. The maid bled her famous employer white until he could no longer pay her the hush money.