Extremely violent and intended to kill, or used to describe something extremely difficult or unpleasant.
From Middle English 'murdre' (murder), combined with the suffix '-ous' (full of, characterized by). The root 'murd' comes from Old English 'morthor'. The metaphorical sense of 'extremely difficult' (like a 'murderous' schedule) emerged in the 20th century.
Interestingly, we use 'murderous' for things that have nothing to do with actual killing—a 'murderous heat wave' or 'murderous schedule'—showing how powerful language lets us express intensity by comparing difficult things to something deadly.
Complete word intelligence in one call. Free tier — 50 lookups/day.