We use 3D simulations to demonstrate that high-quality ultra-relativistic electron bunches can be generated upon reflection of a twisted laser beam off a plasma mirror. The unique topology of the beam with a twist index $|l| = 1$ creates an accelerating structure dominated by longitudinal laser electric and magnetic fields in the near-axis region. We show that the magnetic field is essential for creating a train of dense mono-energetic bunches. For a 6.8~PW laser, the energy reaches 1.6~GeV with a spread of 5.5%. The bunch duration is 320 as, its charge is 60~pC and density is $sim 10^{27}$~m$^{-3}$. The results are confirmed by an analytical model for the electron energy gain. These results enable development of novel laser-driven accelerators at multi-PW laser facilities.
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