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I use the following code to manually draw arrows from one table cell to another.

documentclass{beamer}

beamertemplatenavigationsymbolsempty

usepackage{verbatim}

usepackage{tikz}

usepackage{pgfplots}

usetikzlibrary{arrows, arrows.meta, positioning}

begin{document}

begin{frame}[t]

frametitle{}

begin{minipage}{textwidth}

begin{table}

begin{tabular}{*6{c}}

15.1 & 23.7 & 19.7 & 15.4 & 18.3 & 23.0\

17.4 & 18.6 & 12.9 & 20.3 & 13.7 & 21.4\

10.3 & 26.1 & 15.7 & 14.0 & 17.8 & 33.8\

23.2 & 12.9 & 29.8 & 18.3 & 14.2 & 20.8\

13.5 & 17.1 & 20.7 & 27.1 & 18.9 & 16.6\

end{tabular}

end{table}

begin{minipage}{textwidth}

begin{tikzpicture}[overlay]

draw<2-> [ultra thick, blue, latex'-] (4.1,1.66) -- +(0:.4);

draw<3-> [ultra thick, red, -latex'] (5.2,2.66) -- +(-74:1.4);

end{tikzpicture}

end{minipage}

end{minipage}

end{frame}

end{document}

Is it possible to automate drawing the arrows from one table cell to another, using cell references instead of manually drawing them?

Something like this?

documentclass[tikz]{standalone}

usetikzlibrary{matrix}

begin{document}

begin{tikzpicture}

matrix (x) [matrix of nodes,row sep=1em,column sep=1em] {%

15.1 & 23.7 & 19.7 & 15.4 & 18.3 & 23.0\

17.4 & 18.6 & 12.9 & 20.3 & 13.7 & 21.4\

10.3 & 26.1 & 15.7 & 14.0 & 17.8 & 33.8\

23.2 & 12.9 & 29.8 & 18.3 & 14.2 & 20.8\

13.5 & 17.1 & 20.7 & 27.1 & 18.9 & 16.6\};

draw[->] (x-2-1) -- (x-4-5);

% Node names: (<name of matrix>-<row>-<column>)

end{tikzpicture}

end{document}

In beamer, there may be some problems with matrix, as described here. Taking solutions from that question we have for example

documentclass{beamer}

beamertemplatenavigationsymbolsempty

usepackage{verbatim}

usepackage{tikz}

usetikzlibrary{arrows, arrows.meta, positioning, matrix}

begin{document}

begin{frame}[fragile]

frametitle{}

begin{minipage}{textwidth}

centering

begin{tikzpicture}

matrix (x) [matrix of nodes,row sep=1em,column sep=1em] {%

15.1 & 23.7 & 19.7 & 15.4 & 18.3 & 23.0\

17.4 & 18.6 & 12.9 & 20.3 & 13.7 & 21.4\

10.3 & 26.1 & 15.7 & 14.0 & 17.8 & 33.8\

23.2 & 12.9 & 29.8 & 18.3 & 14.2 & 20.8\

13.5 & 17.1 & 20.7 & 27.1 & 18.9 & 16.6\};

draw<2-> [->] (x-2-1) -- (x-4-5);

end{tikzpicture}

end{minipage}

end{frame}

end{document}

Matrix is not really designed to draw a table, so drawing border lines is a bit tricky.

documentclass[tikz,margin=1mm]{standalone}

usetikzlibrary{matrix,calc}

begin{document}

begin{tikzpicture}

matrix (x) [matrix of nodes,row sep=1em,column sep=1em] {%

15.1 & 23.7 & 19.7 & 15.4 & 18.3 & 23.0\

17.4 & 18.6 & 12.9 & 20.3 & 13.7 & 21.4\

10.3 & 26.1 & 15.7 & 14.0 & 17.8 & 33.8\

23.2 & 12.9 & 29.8 & 18.3 & 14.2 & 20.8\

13.5 & 17.1 & 20.7 & 27.1 & 18.9 & 16.6\};

draw[->] (x-2-1) -- (x-4-5);

% Node names: (<name of matrix>-<row>-<column>)

foreach i in {1,...,6} 

    draw ($(x-1-i.north west)+(-.5em,.5em)$) -- ($(x-5-i.south west)+(-.5em,-.5em)$);

foreach i in {1,...,5} 

    draw ($(x-i-1.south west)+(-.5em,-.5em)$) -- ($(x-i-6.south east)+(.5em,-.5em)$);

draw ($(x-1-1.north west)+(-.5em,.5em)$) -| ($(x-5-6.south east)+(.5em,-.5em)$);

end{tikzpicture}

end{document}

The obligatory tikzmark and beamer-overlay-styles answer. It might be more useful if you use more features of table, which are harder to reproduce with a tikz matrix.

documentclass{beamer}

beamertemplatenavigationsymbolsempty

usepackage{verbatim}

usepackage{tikz}

usetikzlibrary{tikzmark,overlay-beamer-styles}

usetikzlibrary{arrows}

begin{document}

begin{frame}[t]

frametitle{}

begin{table}

begin{tabular}{*6{c}}

15.1 & 23.7 & tikzmarknode{m13}{19.7} & 15.4 & 18.3 & 23.0\

17.4 & 18.6 & 12.9 & 20.3 & 13.7 & 21.4\

10.3 & tikzmarknode{m32}{26.1} & tikzmarknode{m33}{15.7} & 14.0 & 17.8 & 33.8\

23.2 & 12.9 & 29.8 & tikzmarknode{m44}{18.3} & 14.2 & 20.8\

13.5 & 17.1 & 20.7 & 27.1 & 18.9 & 16.6\

end{tabular}

end{table}

begin{tikzpicture}[remember picture,overlay]

draw[ultra thick, blue, -latex',visible on=<2->] (m13.south east) -- (m44.north west);

draw[ultra thick, red, -latex',visible on=<3->] (m33) -- (m32);

end{tikzpicture}

end{frame}

end{document}