Observations of ultra-diffuse galaxies NGC 1052-DF2 and -DF4 show they may contain little dark matter, challenging our understanding of galaxy formation. Using controlled N-body simulations, we explore the possibility that their properties can be reproduced through tidal stripping from the elliptical galaxy NGC 1052, in both cold dark matter (CDM) and self-interacting dark matter (SIDM) scenarios. To explain the dark matter deficiency, we find that a CDM halo must have a very low concentration so that it can lose sufficient inner mass in the tidal field. In contrast, SIDM favors a higher and more reasonable concentration as core formation enhances tidal mass loss. Final stellar distributions in our SIDM benchmarks are more diffuse than the CDM one, and hence the former are in better agreement with the data. We further show that a cored CDM halo model modified by strong baryonic feedback is unlikely to reproduce the observations. Our results indicate that SIDM is more favorable for the formation of dark-matter-deficient galaxies.