From Longman Dictionary of Contemporary Englishbeaver away phrasal verb informalWORK HARDto work very hard, especially at writing or calculating something at He’s been beavering away at his homework for hours. → beaver→ See Verb table
Examples from the Corpus
beaver away• To do the work requires an enormous amount of effort beavering away among old records, checking, copying and encoding.• Information can be automatically kept up to date, and will allow individuals to co-operate on projects instead of beavering away in isolation.• Haven't you finished? You've been beavering away on that report all morning.• You will enjoy beavering away to find out. 