  Magnetars are a special subset of the isolated neutron star family, with
X-ray and radio emission mainly powered by the decay of their immense magnetic
fields. Many attributes of magnetars remain poorly understood: spin-down
glitches or the sudden reductions in the star's angular momentum, radio bursts
reminiscent of extra-galactic Fast Radio Bursts (FRBs), and transient pulsed
radio emission lasting months to years. Here we unveil the detection of a large
spin-down glitch event ($|\Delta\nu/\nu| = 5.8_{-1.6}^{+2.6}\times10^{-6}$)
from the magnetar SGR~1935+2154 on 2020 October 5 (+/- 1 day). We find no
change to the source persistent surface thermal or magnetospheric X-ray
behavior, nor is there evidence of strong X-ray bursting activity. Yet, in the
subsequent days, the magnetar emitted three FRB-like radio bursts followed by a
month long episode of pulsed radio emission. Given the rarity of spin-down
glitches and radio signals from magnetars, their approximate synchronicity
suggests an association, providing pivotal clues to their origin and triggering
mechanisms, with ramifications to the broader magnetar and FRB populations. We
postulate that impulsive crustal plasma shedding close to the magnetic pole
generates a wind that combs out magnetic field lines, rapidly reducing the
star's angular momentum, while temporarily altering the magnetospheric field
geometry to permit the pair creation needed to precipitate radio emission.
