This might appeal to you.
\documentclass{article}
\usepackage{amsmath}
\DeclareMathSymbol{\smallslash}{\mathord}{operators}{32}
\newcommand{\negexcl}{\mathrel{\smallslash\mkern-5mu{!}}}
\begin{document}
$a\negexcl b$
$a\mathrel{!}b$
\end{document}

A different implementation, with the slash similar to \nmid. The first line shows that the two slashes coincide. The color package is only used for that example.
The symbol won't change according to the math style. It's left as an exercise to adapt it for subscripts and superscripts.
\documentclass{article}
\usepackage{amsmath,amssymb,pict2e,picture}
\usepackage{color}
\newcommand{\negexcl}{\mathrel{\smallslash{!}}}
\makeatletter
\newcommand{\smallslash}{%
\begingroup
\sbox\z@{$\m@th\mkern1mu$}%
\dimen@=\wd\z@
\begin{picture}(0,0)
\roundcap
\put(0,\fontdimen22\textfont2){\line(1,0.9){5\dimen@}}
\end{picture}%
\endgroup
}
\makeatother
\begin{document}
{\ooalign{\color{red}$\negexcl$\cr$\nmid$\cr}}
{\ooalign{$\nmid$\cr\color{red}$\negexcl$\cr}}
$a\negexcl b\nmid c$
$a\mathrel{!}b\mid c$
\end{document}

$\not{!}$a too long slash? – CarLaTeX May 26 '17 at 17:12