How to Get a Cut in Timeline?

You could use a \multicolumn to overwrite the general column specification. In the column I used \rotatexbox to get three dots below each other and \hspace to align them with the time line. You may adjust the values to your needs.

\documentclass[xcolor={x11names,table}]{beamer}

\usepackage[utf8]{inputenc}
\usepackage[english]{babel}

\usepackage[TS1,T1]{fontenc}
\usepackage{fourier, heuristica}
\usepackage{array, booktabs}

\newcommand{\foo}{%
   \color{LightSteelBlue3}%
   \makebox[0pt]{\textbullet}%
   \hskip-0.5pt\vrule width 1pt%
   \hspace{\labelsep}%
}

\newlength{\CVbreakdotsep}% length to change spacing between dots
\setlength{\CVbreakdotsep}{0.6mm}

\newcommand{\CVbreakdot}{% command for smaller dots
   \scalebox{0.6}{\textbullet}%
}

\newcommand{\CVbreak}{% command for the break itself
   \multicolumn{2}{l}{%
      \hspace*{8.715mm}% <--- align dots with vertical line
      \rotatebox[origin=c]{-90}{%
         \color{LightSteelBlue3}%
         \hspace{2mm}% <--- extra vertical (horizontal–90°) space
         \CVbreakdot\kern\CVbreakdotsep\CVbreakdot\kern\CVbreakdotsep\CVbreakdot
         \hspace{2mm}% <--- extra vertical (horizontal–90°) space
      }%
   } \\%
}

\begin{document}

\begin{frame}
\begin{table}
   \renewcommand\arraystretch{1.4}
   \arrayrulecolor{LightSteelBlue3}
   \begin{tabular}{@{\,}r <{\hskip 2pt} !{\foo} >{\raggedright\arraybackslash}p{5cm}}
      \toprule
      \addlinespace[1.5ex]
      1969 & Lassa virus. \\
      \CVbreak
      1989 & Guanarito virus, Venezuela. \\
   \end{tabular}
\end{table}
\end{frame}

\end{document} 

---

smaller spaces:

\documentclass[xcolor={x11names,table}]{beamer}

\usepackage[utf8]{inputenc}
\usepackage[english]{babel}

\usepackage[TS1,T1]{fontenc}
\usepackage{fourier, heuristica}
\usepackage{array, booktabs}

\newcommand{\foo}{%
   \color{LightSteelBlue3}%
   \makebox[0pt]{\textbullet}%
   \hskip-0.5pt\vrule width 1pt%
   \hspace{\labelsep}%
}

\newlength{\CVbreakdotsep}% length to change spacing between dots
\setlength{\CVbreakdotsep}{0.1mm}

\newcommand{\CVbreakdot}{% command for smaller dots
   \scalebox{0.4}{\textbullet}% % 0.6 too big!
}

\newcommand{\CVbreak}{% command for the break itself
   \multicolumn{2}{l}{%
      \hspace*{8.97mm}% <--- align dots with vertical line
      \rotatebox[origin=c]{-90}{%
         \color{LightSteelBlue3}%
         \hspace{-5.5mm}% <--- extra vertical (horizontal–90°) space;
         \CVbreakdot\kern\CVbreakdotsep\CVbreakdot\kern\CVbreakdotsep\CVbreakdot
      }%
   } \\[-3.6mm]%
}

\begin{document}

\begin{frame}
\begin{table}
   \renewcommand\arraystretch{1.4}
   \arrayrulecolor{LightSteelBlue3}
   \begin{tabular}{@{\,}r <{\hskip 2pt} !{\foo} >{\raggedright\arraybackslash}p{5cm}}
      \toprule
      \addlinespace[1.5ex]
      1969 & Lassa virus. \\
      \CVbreak
      1989 & Guanarito virus, Venezuela. \\
   \end{tabular}
\end{table}
\end{frame}

\end{document} 

Here is a solution with the nccrules package. I define a \vdashrule, slightly thinner than the rule of the time line, and a \addvdashrule commands. The parameters for the vertical dashline are specific to this context but can easily be adapted to another. You can stack vertical dashlines.

\documentclass[xcolor={x11names, table}]{beamer}
% http://tex.stackexchange.com/a/196808/13173
% http://tex.stackexchange.com/a/303021/13173

\usepackage[utf8]{inputenc}
\usepackage[english]{babel}

\usepackage[TS1,T1]{fontenc}
\usepackage{fourier, erewhon}
\usepackage{array, booktabs}
\usepackage{nccrules}
\usepackage{caption}
\DeclareCaptionFont{blue}{\color{LightSteelBlue3}}

\newcommand{\foo}{\color{LightSteelBlue3}\makebox[0pt]{{\textbullet}}\hskip-0.5pt\vrule width 1pt}
\newcommand\vdashrule{\color{LightSteelBlue3}\dashrule[-0.75ex]{0.8}{2.5 2 2.5 2 2.5 2 2.5}}%
\newcommand\addvdashrule{%
 \multicolumn{1}{@{}r@{}}{\begin{tabular}{@{\,}r <{\hskip 2pt} !{\hspace{\labelsep}\hskip-0.5pt \vdashrule\hskip0.1pt }}~\end{tabular}}}%

\begin{document}

\begin{frame}
    \begin{table}
    \renewcommand\arraystretch{1.4}\arrayrulecolor{LightSteelBlue3}
    \captionsetup{singlelinecheck=false, font=blue, labelfont=sc, labelsep=quad}
    \caption{Timeline}\vskip -1.5ex
        \begin{tabular}{@{\,}r <{\hskip 2pt} !{\foo} >{\raggedright\arraybackslash}p{5cm}}
        \toprule
        \addlinespace[1.5ex]
        1969 & Lassa virus. \\%
        \addvdashrule \\[-0.4ex]
         \addvdashrule \\
         1989 & Guanarito virus, Venezuela. 1993 - Sabia virus (BrHF), Brazil. 2004 - \end{tabular}
    \end{table}
\end{frame}

\end{document} 

well, rather a quick hack, than a solution, but perhaps it does, what you want.

\documentclass[xcolor=x11names,table]{beamer}
% http://tex.stackexchange.com/a/196808/13173
% http://tex.stackexchange.com/a/303021/13173

\usepackage[utf8]{inputenc}
\usepackage[english]{babel}

\usepackage[TS1,T1]{fontenc}
\usepackage{fourier, heuristica}
\usepackage{array, booktabs}
\usepackage{caption}
\DeclareCaptionFont{blue}{\color{LightSteelBlue3}}

\newcommand{\foo}{\color{LightSteelBlue3}\makebox[0pt]{\textbullet}\hskip-0.5pt\vrule width 1pt\hspace{\labelsep}}

\begin{document}

    \begin{frame}
        \begin{table}
            \renewcommand\arraystretch{1.4}\arrayrulecolor{LightSteelBlue3}
            \captionsetup{font=blue, labelfont=sc, labelsep=quad}
            \caption{Timeline}\vskip -1.5ex
            \begin{tabular}{@{\,}r <{\hskip 2pt} !{\foo} >{\raggedright\arraybackslash}p{5cm}}
                \toprule
                \addlinespace[1.5ex]
                1969 & Lassa virus.
            \end{tabular}

            \begin{tabular}{@{\,}r <{\hskip 2pt} !{\color{LightSteelBlue3}\makebox[0pt]{\textbullet\textbullet\textbullet}} >{\raggedright\arraybackslash}p{4.4cm}}
                {} & {}
            \end{tabular}

            \begin{tabular}{@{\,}r <{\hskip 2pt} !{\foo} >{\raggedright\arraybackslash}p{5cm}}
                1989 & Guanarito virus, Venezuela. 1993 - Sabia virus (BrHF), Brazil. 2004 - \end{tabular}
        \end{table}
    \end{frame}

\end{document}