We report on an electron accelerator based on few-cycle (8 fs full width at half maximum) laser pulses, with only 40 mJ energy per pulse, which constitutes a previously unexplored parameter range in laser-driven electron acceleration. The produced electron spectra are monoenergetic in the tens-of-MeV range and virtually free of low-energy electrons with thermal spectrum. The electron beam has a typical divergence of 5-10 mrad. The accelerator is routinely operated at 10 Hz and constitutes a promising source for several applications. Scalability of the few-cycle driver in repetition rate and energy implies that the present work also represents a step towards user friendly laser-based accelerators.