  This paper studies complete non-compact smooth metric measure space
$(M^n,g,\mathrm{e}^{-f}\mathrm{d}v)$ with positive first spectrum
$\lambda_1(\Delta_f)$ or satisfying a weighted Poincar\'e inequality with
weight function $\rho$. We establish two splitting and vanishing theorems for
$L_f^p$ harmonic $1$-forms under the assumption that $m$-Bakry-\'Emery Ricci
curvature $\mathrm{Ric}_{m,n}\geq -a\lambda_1(\Delta_f)$ or
$\mathrm{Ric}_{m,n}\geq -a\rho-b$ for particular constants $a$ and $b>0$. These
results are inspired by the work of Han-Lin and are $L_f^p$ generalizations of
previous works by Dung-Sung and Vieira for $L^2$ harmonic $1$-forms.
