The lengths you are looking for are stored in macros \Gm@lmargin
(distance between left margin of paper and left border of text area) and \Gm@rmargin
(distance between right border of text area and right margin of paper), so \paperwidth=\Gm@lmargin+\textwidth+\Gm@rmargin
. Since the \Gm@...
are macros, you can define some lengths first to easily use them in \dimexpr
(see remark at the end):
\documentclass[t]{beamer}
\usepackage{lipsum}
\usepackage{geometry}
\geometry{paperwidth=250mm,paperheight=190.5mm,left=0mm,right=0mm,top=0mm,bottom=0mm}
\setbeamersize{text margin left=10mm,text margin right=60mm}
\makeatletter
\newlength\beamerleftmargin
\newlength\beamerrightmargin
\setlength\beamerleftmargin{\Gm@lmargin}
\setlength\beamerrightmargin{\Gm@rmargin}
\makeatother
\begin{document}
\begin{frame}
\textcolor{blue}{\rule{\textwidth}{3pt}}
\textcolor{red}{\rule{\dimexpr\paperwidth-\beamerleftmargin-\beamerrightmargin\relax}{3pt}}% 180mm = 250mm - 10mm - 60mm
\end{frame}
\end{document}

If a sidebar is used by the theme, some other horizontal lengths will have to be taken into account: \beamer@leftsidebar
, \beamer@rightsidebar
store
the (horizontal) sizes of the side bars, and \beamer@leftmargin
, \beamer@rightmargin
store the distance between sidebar and text.
As jfbu has noticed in his comment
it is not mandatory to define two new length registers and one could do
\def\beamerleftmargin{\dimexpr\Gm@lmargin\relax}
\def\beamerrightmargin{\dimexpr\Gm@rmargin\relax}