Hi Will,
I've been here - it's possible but non-obvious! I assume that you want to export a vertical plane - a 2D vertical transect through the water column. Note that these instructions refer to MIKE 2012 - I don't know what may have changed in the 2014 edition.
First you must get your model to output a 3D .dfsu file, a "Volume" file. There is no way to get directly to a vertical plane.
Having done this, create a two-line .xyz file with the start and end coordinates of the transect that you want. It doesn't matter what the z-values are, they will be ignored, but they need to be there. I usually just set them to zero.
Open your .dfsu in Data Manager, and go to Tools -> Extract. Under "Dimension" select "Profile". Under "Profile" select "Load from .xyz file".
The rest is obvious, except for "Nearest segment list". If you leave this unchecked, then MIKE will interpolate to estimate the correct values on your line. If you check it, then as I understand it instead of doing this it will simply use the values for each mesh element that the line passes through, even though the centres of those elements may not lie on the line.. This will run much faster, but may be less accurate.
Hope that helps, and that it's still relevant four months later (and anyway, it may apply to others).