In R2020a and later releases, you can export and copy UIFIgure and UI Axes directly.
exportgraphics
copygraphics
From R2020b, you use exportapp function when exporting UIFigure.
If you use R2019b and earlier releases, please refer the following information.
UI Figures and UI Axes support only a subset of the properties that traditional figures and axes support. UI Figures and UI Axes do not support properties for printing, saving, callback execution, or custom mouse and keyboard interaction.
One workaround to save the UI Figures/UI Axes is to copy it to a traditional figure/axes and then save it.
ux = uiaxes;
p = plot(ux,magic(5));
fig1 = figure;
ax = axes;
copyobj(ux.Children,ax);
saveas( fig1,'myplot.png');
Another workaround is to use 'ScreenCapture', a File Exchange pick of the week: https://www.mathworks.com/matlabcentral/fileexchange/24323-screencapture-get-a-screen-capture-of-a-figure-frame-or-component
A blog post about this function can be found here: https://blogs.mathworks.com/pick/2012/08/10/grab-a-screen-shot-from-within-matlab/
Please note that if you have any questions regarding the code in a File Exchange, please contact the author.