Abstract In this paper we present a torsional non-relativi-stic Chern–Simons (super)gravity theory in three spacetime dimensions. We start by developing the non-relativistic limit of purely bosonic relativistic teleparallel formulation gravity. On-shell latter yields non-Riemannian setup with non-vanishing torsion, which, at level, translates into spatial torsion sourced cosmological constant. ...