This seems to be a koine word meaning easy. LSJ has it and the verb κοπάζω, but the English wiktionary didn't have either. I added both to wiktionary. It seems obvious that the etymology of κοπάζω is the same as that of κόπος. Is εὔκοπος from the same root, or is it a false cognate? The meaning seems reversed. I would have expected something like ακοπος. To me, εὔκοπος would naively seem to be a word I would make up to describe the virtuous feeling of being tired after a hard day's work -- not the feeling of not being tired at all.
It is from the same root as κοπάζω, and also from that of the more common verb κόπτω "hit, strike". Presumably it comes from the latter meaning, so that it originally meant something like "easy to hit" (the prefix εὐ- can mean "easy" as well as "good", as in e.g. εὐδιάβατος "easy to cross"), with a later generalization of sense to "easy" tout court.