To threaten to 'have someone's guts for garters' is to state the intention to do them serious harm. The threat isn't an actual and literal one and the overstatement of reprisal is meant to indicate humour, but with an indication that the threatened person has done something which has been something of an annoyance.

What does have your guts mean?

Possess the courage, as in Does he have the guts to dive off the high board? This expression replaces the earlier and now obsolete sense of stomach as “courage,” a usage from the early 1500s. [ Slang; late 1800s]

Where did the phrase I hate your guts come from?

hate (sb's) guts to dislike (sb) intensely. Adopted from the USA around 1937. The New Partridge Dictionary of Slang and Unconventional English (2008) says: guts noun 1 the stomach; the general area of the stomach and intestines.