  In the seconds following their formation in core-collapse supernovae,
"proto"-magnetars drive neutrino-heated magneto-centrifugal winds. Using a
suite of two-dimensional axisymmetric MHD simulations, we show that relatively
slowly rotating magnetars with initial spin periods of $P_{\star0}=50-500$ ms
spin down rapidly during the neutrino Kelvin-Helmholtz cooling epoch. These
initial spin periods are representative of those inferred for normal Galactic
pulsars, and much slower than those invoked for gamma-ray bursts and
super-luminous supernovae. Since the flow is non-relativistic at early times,
and because the Alfv\'en radius is much larger than the proto-magnetar radius,
spindown is millions of times more efficient than the typically-used dipole
formula. Quasi-periodic plasmoid ejections from the closed zone enhance
spindown. For polar magnetic field strengths $B_0\gtrsim5\times10^{14}$ G, the
spindown timescale can be shorter than than the Kelvin-Helmholtz timescale. For
$B_0\gtrsim10^{15}$ G, it is of order seconds in early phases. We compute the
spin evolution for cooling proto-magnetars as a function of $B_0$,
$P_{\star0}$, and mass ($M$). Proto-magnetars born with $B_0$ greater than
$\simeq1.3\times10^{15}\,{\rm\,G}\,(P_{\star0}/{400\,\rm\,ms})^{-1.4}(M/1.4\,{\rm
M}_\odot)^{2.2}$ spin down to periods $> 1$ s in just the first few seconds of
evolution, well before the end of the cooling epoch and the onset of classic
dipole spindown. Spindown is more efficient for lower $M$ and for larger
$P_{\star0}$. We discuss the implications for observed magnetars, including the
discrepancy between their characteristic ages and supernova remnant ages.
Finally, we speculate on the origin of 1E 161348-5055 in the remnant RCW 103,
and the potential for other ultra-slowly rotating magnetars.
