We present and publicly release (https://www.gclasshst.com) the first spatially resolved H$alpha$ maps of star-forming cluster galaxies at $zsim1$, made possible with the Wide Field Camera 3 (WFC3) G141 grism on the Hubble Space Telescope (HST). Using a similar but updated method to 3D-HST in the field environment, we stack the H$alpha$ maps in bins of stellar mass, measure the half-light radius of the H$alpha$ distribution and compare it to the stellar continuum. The ratio of the H$alpha$ to stellar continuum half-light radius, $R[mathrm{H}alpha/mathrm{C}]=frac{R_{mathrm{eff, H}alpha}}{R_{mathrm{eff, Cont}}}$, is smaller in the clusters by $(6pm9)%$, but statistically consistent within $1sigma$ uncertainties. A negligible difference in $R[mathrm{H}alpha/mathrm{C}]$ with environment is surprising, given the higher quenched fractions in the clusters relative to the field. We postulate that the combination of high quenched fractions and no change in $R[mathrm{H}alpha/mathrm{C}]$ with environment can be reconciled if environmental quenching proceeds rapidly. We investigate this hypothesis by performing similar analysis on the spectroscopically-confirmed recently quenched cluster galaxies. 87% have H$alpha$ detections, with star formation rates $8pm1$ times lower than star-forming cluster galaxies of similar stellar mass. Importantly, these galaxies have a $R[mathrm{H}alpha/mathrm{C}]$ that is $(81pm8)%$ smaller than coeval star-forming field galaxies at fixed stellar mass. This suggests the environmental quenching process occurred outside-in. We conclude that disk truncation due to ram-pressure stripping is occurring in cluster galaxies at $zsim1$, but more rapidly and/or efficiently than in $zlesssim0.5$ clusters, such that the effects on $R[mathrm{H}alpha/mathrm{C}]$ become observable just after the cluster galaxy has recently quenched.
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