The $q$-digamma function $\psi_q(x)$ and the $q$-polygamma functions $\psi_q^{(r)}(x)$, $r\in\mathbb N=\{1,2,\dots\}$ are defined for all $x>0$ and $0<q<1$. In this paper, the neutrices and the neutrix limit are used to define the $q$-digamma function $\psi_q(x)$ and the $q$-polygamma functions $\psi_q^{(r)}(x)$, $r\in\mathbb N$ for all $x\in\mathbb R$ Moreover, further results are given.