How can I remove the figures from a draft of my document?

I would simply use the endfloat package, which places all floats (figures and tables) at the very end of the document. Then you can print only the leading pages with the text using the page range selection of your PDF viewer.

Alternatively, you can make LaTeX ignore all figure environments using the comment package:

\usepackage{comment}
\excludecomment{figure}
\let\endfigure\relax

See How to exclude text portions by simply setting a variable or option? for more details. A drawback here is that the label references won't work properly.

Just add the draft option when you load your document class, e.g.:

\documentclass[draft]{article}

You can also add the option to the graphicx package:

\usepackage[draft]{graphicx}

---

If you want to save space, you can do as follows:

\renewcommand{\includegraphics}{\relax}

Or if you want to use the ifdraft package, you can do thus:

\documentclass[draft]{article}
\usepackage{ifdraft}
\ifdraft{\renewcommand{\includegraphics}{\relax}}{\relax}

While the draft option replaces all graphics by frames with the same size, you may like to redefine \includegraphics so that it prints only the file name in an \fbox to save space/paper:

\documentclass{article}

\usepackage[demo]{graphicx}
\usepackage{lipsum}

\renewcommand{\includegraphics}[2][]{%
    \fbox{#2}% print file name in a small box
}

\begin{document}
\lipsum[1]
\begin{figure}
    \includegraphics[width=2cm,height=3cm]{imagefile}
    \caption{Caption text}
\end{figure}
\lipsum[2]
\end{document}

Notes

• To suppress the file name box, too, replace the redefinition with \renewcommand{\includegraphics}[2][]{}.

• The option demo lets graphicx print black boxes instead of searching the file to include it. It has nothing to do with your question but is useful for the demonstration ;-)

• The package lipsum provides blind text and doesn’t belong to the solution.