A bunch of solutions with stackengine: I defined \big, Big, &c. variants in two series, based on \varnot + \vert or on \ndivides + \vert with a different \not sign. I suppose it is intended to be a (non-)relational symbol.
\documentclass{article}
\usepackage{mathtools, mathabx, xcolor}
\usepackage{stackengine, relsize}
\newcommand{\nmid}{\mathrel{\stackMath\stackinset{c}{-1.24ex}{c}{}{\varnot}{\vert}}}
\newcommand{\nbmid}{\mathrel{\stackMath\stackinset{c}{-1.24ex}{c}{}{\varnot}{\big\vert}}}
\newcommand{\nBmid}{\mathrel{\stackMath\stackinset{c}{-1.24ex}{c}{}{\varnot}{\Big\vert}}}
\newcommand{\nbbmid}{\mathrel{\stackMath\stackinset{c}{-1.24ex}{c}{}{\varnot}{\bigg\vert}}}
\newcommand{\nBBmid}{\mathrel{\stackMath\stackinset{c}{-1.24ex}{c}{}{\varnot}{\Bigg\vert}}}
%%%
\newcommand{\bndivides}{\mathrel{\stackMath\stackinset{c}{-0.325ex}{c}{}{\notdivides}{\big\vert}}}
\newcommand{\Bndivides}{\mathrel{\stackMath\stackinset{c}{-0.32ex}{c}{}{\notdivides}{\Big\vert}}}
\newcommand{\bbndivides}{\mathrel{\stackMath\stackinset{c}{-0.32ex}{c}{}{\notdivides}{\bigg\vert}}}
\newcommand{\BBndivides}{\mathrel{\stackMath\stackinset{c}{-0.32ex}{c}{}{\notdivides}{\Bigg\vert}}}
\begin{document}
\[ \begin{array}{l*{6}{c}}
\verb+ \nmid series: + & \nmid & \nbmid & \nBmid & \nbbmid & \nBBmid \\[4ex]
\verb+ \ndivides series: + & \ndivides & \bndivides & \Bndivides & \bbndivides & \BBndivides
\end{array} \]
\end{document}

|,\big|,\not|, and\not{\big|}all in the same document? Are you sure your readers can pick up the difference between|and\big|? – Mico May 14 '17 at 12:01|A| | |B|and would like to use|A| \big| |B|to distinguish between the sign of "divides" and that ofcarnality. I know there are other variants such as\mid,\divides, but I really prefer\big|. The only problem is that I would also like to adapt this for "not-dividing", hence my question. – Name May 14 '17 at 12:09