4 images on a frame appearing each a a time - fine tuning beamer

It's not much different than what you have already.

\documentclass{beamer}
\usepackage{mwe} % For dummy images
\usepackage{lmodern} % To suppress some warnings

\begin{document}
\begin{frame}
\centering
\begin{tabular}{c@{}c}
 \includegraphics[width=0.4\textwidth,trim=0 120 160 0,clip]{example-image-a}\pause% 
&\includegraphics[width=0.4\textwidth,trim=160 120 0 0,clip]{example-image-a}\\[-1.5mm]\pause%
 \includegraphics[width=0.4\textwidth,trim=0 0 160 120,clip]{example-image-a}\pause%
&\includegraphics[width=0.4\textwidth,trim=160 0 0 120,clip]{example-image-a}
\end{tabular}

\end{frame}
\end{document}

The trimming might not be good as I did it by eyeballing.

EDIT For the custom image, the following trim values seem to work.

\documentclass{beamer}
\usepackage{graphicx}
\usepackage{lmodern} % To suppress some warnings

\begin{document}
\begin{frame}
\centering
\begin{tabular}{c@{}c}
 \includegraphics[width=0.3\textwidth,trim=0 270 260 0,clip]{SRSF1_details_1fig}\pause% 
&\includegraphics[width=0.3\textwidth,trim=260 270 0 0,clip]{SRSF1_details_1fig}\\[-1.5mm]\pause%
 \includegraphics[width=0.3\textwidth,trim=0 0 260 265,clip]{SRSF1_details_1fig}\pause%
&\includegraphics[width=0.3\textwidth,trim=260 0 0 265,clip]{SRSF1_details_1fig}
\end{tabular}

\end{frame}
\end{document}

You could use TikZ and put the pictures in nodes. With no inner sep or outer sep they align perfectly. If you need spacing, you can use <position>=<distance>, like above right=3mm

Code

\documentclass{beamer}
\usepackage{tikz}

\begin{document}

\begin{frame} \frametitle{Cufflinks analysis - SRSF1}
  \begin{figure}[t]
    \begin{center}
        \begin{tikzpicture}
                \node[above right,inner sep=0,outer sep=0] {\includegraphics[scale=0.7]{test}};\pause
                \node[above left,inner sep=0,outer sep=0] {\includegraphics[scale=0.65]{test}};\pause
                \node[below right,inner sep=0,outer sep=0] {\includegraphics[scale=0.75]{test}};\pause
                \node[below left=0.5cm,inner sep=0,outer sep=0] {\includegraphics[scale=0.6]{test}};
            \end{tikzpicture}
    \end{center}
  \end{figure}
\end{frame}

\end{document}

Result