"To slow the bleeding" means to take actions or measures to reduce or stop a negative situation or loss from getting worse or having a major impact. Full definition
If there is an open wound or active bleeding, a light wrap can be placed to help protect the wound and to help slow bleeding. (petmedicalfresno.com)
The concept is the same as when a baby nurses right after birth, stimulating contractions, which slows bleeding. (americanpregnancy.org)
The greater Los Angeles D.M.A. has painted a picture of newspaper dysfunction, with multiple bankruptcies, slow bleeding of staff resources and the soap opera that Aaron Kushner's attempted turnaround of the Orange County Register all figuring in the tragicomedy. (newsonomics.com)