  We investigate the effects of self-interacting dark matter (SIDM) on the
tidal stripping and evaporation of satellite galaxies in a Milky Way-like host.
We use a suite of five zoom-in, dark-matter-only simulations, two with
velocity-independent SIDM cross sections, two with velocity-dependent SIDM
cross sections, and one cold dark matter simulation for comparison. After
carefully assigning stellar mass to satellites at infall, we find that stars
are stripped at a higher rate in SIDM than in CDM. In contrast, the total bound
dark matter mass loss rate is minimally affected, with subhalo evaporation
having negligible effects on satellites for viable SIDM models. Centrally
located stars in SIDM haloes disperse out to larger radii as cores grow.
Consequently, the half-light radius of satellites increases, stars become more
vulnerable to tidal stripping, and the stellar mass function is suppressed. We
find that the ratio of core radius to tidal radius accurately predicts the
relative strength of enhanced SIDM stellar stripping. Velocity-independent SIDM
models show a modest increase in the stellar stripping effect with satellite
mass, whereas velocity-dependent SIDM models show a large increase in this
effect towards lower masses, making observations of ultra-faint dwarfs prime
targets for distinguishing between and constraining SIDM models. Due to small
cores in the largest satellites of velocity-dependent SIDM, no identifiable
imprint is left on the all-sky properties of the stellar halo. While our
results focus on SIDM, the main physical mechanism of enhanced tidal stripping
of stars apply similarly to satellites with cores formed via other means.
