To cut someone loose means to let them go, usually from a relationship. Think of it this way: if two people are dating, or married, they have imaginary "strings" or "bonds" that connect them together. If you say to someone, "cut me loose" you are asking them cut those strings that attach them to you so you can leave. This phrase isn't always in the context of a romantic relationship, but that's certainly the case here.

Thanks.

It is kinda equivalent to "get rid of st or SB"