  In this paper we present a torsional non-relativistic Chern-Simons
teleparallel (super)gravity theory in three spacetime dimensions. We start by
developing the non-relativistic limit of the purely bosonic relativistic
teleparallel Chern-Simons formulation of gravity. On-shell the latter yields a
non-Riemannian setup with non-vanishing torsion, which, at non-relativistic
level, translates into a non-vanishing spatial torsion sourced by the
cosmological constant. Then we consider the three-dimensional relativistic
$\mathcal{N}=2$ Chern-Simons supergravity theory and obtain its
non-relativistic counterpart by exploiting a Lie algebra expansion method. The
non-relativistic supergravity theory is characterized, on-shell, by a
non-vanishing spatial super-torsion, again sourced by the cosmological
constant.
