Managing checkbox representation

Why not use the already available \boxtimes?

\documentclass{article}
\usepackage{amssymb}
\begin{document}

$\boxtimes$

\end{document}

Here is another possibility:

\documentclass{article}
\usepackage{amssymb,tikz,pdftexcmds,xparse}

\tikzset{box/.style={
    minimum size=0.225cm,
    inner sep=0pt,
    draw,
  },  
  insert mark/.style={
    append after command={%
         node[inner sep=0pt,#1]
           at (\tikzlastnode.center){$\checkmark$}
     }     
  },
  insert bad mark/.style={
    append after command={%
         [shorten <=\pgflinewidth,shorten >=\pgflinewidth]
         (\tikzlastnode.north west)edge[#1](\tikzlastnode.south east)
         (\tikzlastnode.south west)edge[#1](\tikzlastnode.north east)
     }     
  },
}

\makeatletter
\NewDocumentCommand{\tikzcheckmark}{O{} m}{%
  \ifnum\pdf@strcmp{#2}{mark}=\z@%
    \tikz[baseline=-0.5ex]\node[box,insert mark={#1},#1]{};%
  \fi%
  \ifnum\pdf@strcmp{#2}{bad mark}=\z@%
    \tikz[baseline=-0.5ex]\node[box,insert bad mark={#1},#1]{};%
  \fi%
  \ifnum\pdf@strcmp{#2}{no mark}=\z@%
    \tikz[baseline=-0.5ex]\node[box,#1]{};%
  \fi%
}
\makeatother

\begin{document}


\tikzcheckmark[scale=0.75]{mark}\quad\tikzcheckmark[scale=0.75]{no mark}\quad\tikzcheckmark[scale=0.75]{bad mark}

\vspace{1cm}

\tikzcheckmark{mark}\quad\tikzcheckmark{no mark}\quad\tikzcheckmark{bad mark}

\vspace{1cm}

\tikzcheckmark[scale=2,red]{mark}\quad\tikzcheckmark[scale=2,red]{no mark}\quad\tikzcheckmark[scale=2,red]{bad mark}

\end{document}

The result: