How to draw over an picture in TikZ?

If you're talking about the circle with the m in it, it is not behind the rod, but it isn't filled either -- it consists of a black circle with the letter m in it. Add fill=white to the node settings.

\documentclass{scrartcl}
\usepackage{stanli}
\begin{document}

  \begin{tikzpicture}
    %the points
    \point{above}{0}{5};
    \point{above_middle}{0}{4};
    \point{below_middle}{0}{1};
    \point{below}{0}{0};
    %the rod
    \beam{2}{above}{above_middle};
    \beam{2}{below}{below_middle};
    %the support
    \support{1}{above}[180];
    \hinge{1}{above};
    %the mass
    \node at (below) [circle, draw,fill=white] {$m$}; % <----- added fill=white
    %the free body diagram (for the rod)
    %S
    \point{S}{0}{3};
    \load{1}{S}[90];
    \notation{1}{S}{$S$};
    %-S
    \point{-S}{0}{2};
    \load{1}{-S}[-90];
    \notation{1}{-S}{$S$}[below right];
  \end{tikzpicture}

A PSTricks solution.

\documentclass[pstricks]{standalone}
\usepackage{pst-node}

\begin{document}
\begin{pspicture}(-1,.2)(1,-4.4)
    % top part
    \psframe[fillstyle=vlines,hatchsep=1pt,linestyle=none](-1,.2)(1,0)
    \psline(-1,0)(1,0)
    \pnode(-.5,0){L}
    \pnode(.5,0){R}
    \pnode(0,-2){S}
    \rput(0,-1){\Cnode[radius=5pt]{C}}
    \ncline{L}{C}
    \ncline{C}{R}
    \ncline{->}{C}{S}
    \naput[npos=1]{$S$}
    % bottom part
    \pnode(0,-3){S'}
    \rput(0,-4){\Circlenode[radius=10pt]{m}{$m$}}
    \ncline{->}{m}{S'}\nbput[npos=1]{$S$}
\end{pspicture}
\end{document}