  We study the growth rate of matter perturbations in the context of
teleparallel dark energy in a flat universe. We investigate the dynamics of
different theoretical scenarios based on specific forms of the scalar field
potential. Allowing for non-minimal coupling between torsion scalar and scalar
field, we perform a phase-space analysis of the autonomous systems of equations
through the study of critical points. We thus analyze the stability of the
critical points, and discuss the cosmological implications searching for
possible attractor solutions at late times. Furthermore, combing the growth
rate data and the Hubble rate measurements, we place observational constraints
on the cosmological parameters of the models through Monte Carlo numerical
method. We find that the scenario with a non-minimal coupling is favoured with
respect to the standard quintessence case. Adopting the best-fit results, we
show that the dark energy equation of state parameter can cross the phantom
divide. Finally, we compare our results with the predictions of the concordance
$\Lambda$CDM paradigm by performing Bayesian model selection.
