Green’s Dictionary of Slang

blue murder n.

also bloody murder
[blue adj.5 + SE murder]

1. [mid-19C+] cries of terror, horror, alarm; usu. in phrs. below.

2. attrib. use of sense 1.

In phrases

like blue murder (adv.) [mid-19C+]

1. to a great extent; very much.

2. (also like blue stink) very quickly, at top speed.

3. very aggressively.

out for blue murder (adj.)

[1950s] very angry.

scream blue murder (v.) (also holler blue murder, shout..., yell…, scream bloody murder)

[mid-19C+] to be in a state of hysteria, utterly and completely overwrought or terrified.