  In this paper, we investigate the late-time cosmic acceleration in mimetic
$f(R,T)$ gravity with Lagrange multiplier and potential in a Universe
containing, besides radiation and dark energy, a self-interacting (collisional)
matter. We obtain through the modified Friedmann equations, the main equation
that can describe the cosmological evolution and with several models from
$Q(z)$ and the well known particular model $f(R, T)$, we perform an analysis of
the late-time evolution. We examine the behavior of the Hubble parameter, the
dark energy equation of state and the total effective equation of state and we
compare in each case the resulting picture with the non-collisional matter
(assumed as dust) and also with the collisional matter in mimetic $f(R, T)$
gravity. The results obtained are in good agreement with the observational data
and show that in presence of the collisional matter the dark energy
oscillations in mimetic f(R, T) gravity can be damped.
