Simple answer: With xtrings is as simple as \StrGobbleLeft{\the\year}{2}.
Not so simple answer: In the example below, the \sy ("short year") macro as is extract the two digits from the actual default year (i.e, 14) or from an optional argument (e.g. \sy[1939]).
This argument also change \the\year for later use (e.g. in \today to obtain October 9,1939)., but if you do not like that feature is quite obvious how remove it.
Finally, as I cannot imagine the benefit of using a two digit format for dates outside the XX or XXI century in real life, the argument only work with 4 digits in order to detect typing mistakes (otherwise print a warning box) with the help of the xifthen package. If you do not like this feature either, go to the simple answer.
\documentclass{article}
\usepackage{xstring,xifthen}
\newcommand{\sy}[1][]{
\StrLen{#1}[\yearlength]%
\ifthenelse{\yearlength = 4}% Only 4 character allowed
{\year#1\relax\StrGobbleLeft{#1}{2}}%
{\ifthenelse{\yearlength = 0} % What by default
{\StrGobbleLeft{\the\year}{2}}%
{\fbox{\bfseries\ttfamily OOPS! typed #1}}}}%
\begin{document}
Really today is \today.\par
% Correct use with default year
World War III will start after \sy\ (... the year \the\year, obviously).\par
% Mistyped date that go to Roman times, so year is not changed.
World War II started in the \sy[193]\ (... still stuck in \the\year).\par
% Correct use with fixed year
World War I started in \sy[1914]\ (we mean now \the\year !).\par
Now \verb|\the\year| is still \the\year, and \verb|\today| is \today.\par
% Mistyped date that go to Star Trek era, so year is not changed.
Franco-Prussian war started in \sy[18870].\par
\end{document}

\twodigitis used to guarantee that a number is shown with at least two digits, not at most ;-) – Oct 08 '14 at 19:07