You need to save the title and label parameters and use them later. (Also, \ label should appear after \ caption.)
Something like this should work:
\newcommand{\templabel}{}% stores the label
\newcommand{\tempcaption}{}% stores the caption
\newenvironment{mytable}[3]{%
\gdef\templabel{
\gdef\tempcaption{
\begin{table}[hbtp]%
\begin{center}%
\begin{tabular}{
}{%
\caption{\tempcaption}% use the stored caption
\label{\templabel}% use the stored label (*after* the caption)
\end{tabular}%
\end{center}%
\end{table}%
}
Use the following environment:
\begin{mytable}{tab:example}{This is the caption for my example table.}{cc}
Row 1 & First \\
Row 2 & Second \\
Row 3 & Third \\
\end{mytable}
I have not tested this code.