There are some submissions on file exchange for this, like this one: https://www.mathworks.com/matlabcentral/fileexchange/57366-separateaxes
Here's a very crude version, this doesn't tie together labels or automatically adjust position, or lots of other niceties, but gives you an idea about how to fake the general effect:
clf
ax=axes('Position',[.12 .12 .85 .85]);
hold on
t=linspace(0,4*pi,100);
plot(ax,sin(t))
ax_x=axes;
ax_x.Position=ax.Position;
ax_x.Position(2)=.07;
ax_x.Position(4)=.00001;
ax_y=axes;
ax_y.Position=ax.Position;
ax_y.Position(1)=.07;
ax_y.Position(3)=.00001;
ax_x.FontSize = ax.FontSize;
ax_y.FontSize = ax.FontSize;
linkprop([ax ax_x],'FontSize');
linkaxes([ax ax_x],'x')
linkprop([ax ax_y],'FontSize');
linkaxes([ax ax_y],'y')
ax.XColor='none';
ax.YColor='none';
ax.XTick=[];
ax.YTick=[];
