For this task and similar ones, the zref package comes in handy. Based on the abspage and thepage modules provided by this package, you can define a macro \chappagerangelabel as follows:
\documentclass{scrbook}
\usepackage{calc}
\usepackage[abspage, thepage]{zref}
\usepackage{scrpage2}
\usepackage{lipsum}% lorem ipsum placeholder text
\makeatletter
\newcounter{chappagerange}% auxiliary counter
\newcounter{chappointer}% auxiliary counter
\stepcounter{chappointer}% value 1 for first chapter
\newcommand*{\chappagerangelabel}{%
\zref@label{chappagerange:\the\value{chappointer}}%
\setcounter{chappagerange}{\zref@extract{chappagerange:\the\value{chappointer}}{abspage}}%
\edef\thechappagerange{\zthepage{\the\value{chappagerange}}}% first page
\stepcounter{chappointer}%
\setcounter{chappagerange}{\zref@extract{chappagerange:\the\value{chappointer}}{abspage}-1}%
\edef\thechappagerange{pp.~\thechappagerange--\zthepage{\the\value{chappagerange}}}% first page--last page
}
Now, define a macro \pagerangemark modelled after \pagemark:
\DeclareRobustCommand*{\pagerangemark}{%
{\pnumfont\thechappagerange}%
}
\makeatother
Put \chappagerangelabel at the very beginning of each chapter and immediately after the last chapter and use \pagerangemark in \ofoot:
\begin{document}
\pagestyle{scrheadings}
\clearscrheadfoot
\cfoot[\pagemark]{\pagemark}
\chead[]{\headmark}
\frontmatter
\noindent
Text
\mainmatter
\ofoot[\pagerangemark]{\pagerangemark}
\chapter{A Chapter}
\chappagerangelabel
\lipsum[1-20]
\chapter{Another Chapter}
\chappagerangelabel
\lipsum[21-40]
\backmatter
\chappagerangelabel
\ofoot[]{}
\noindent
Text
\end{document}
Note that this solution does not allow for the case that the last page of the last chapter is also the last page of the whole document. Apart from that, it should work smoothly.