"This is a mortar soldier and will try to stay behind his troops and pepper your position with explosive rounds."— Official game quote
Another Wehrmacht given a special weapon, this time to rain hell from the sky on your men. German mortar units will not fire at enemies which are too close to them (in general, anything in the top half will not be targeted). Keep that in mind when you are placing your "meatshields", or the mortars will be targeting the next closest unit behind them! The German mortar units tend to stay in the top 1/3rd of the screen, to pepper your lines. He is one of units that DOESN'T advance. Like the German gunner, he moves shortly in the battlefield, deploys his mortar, and wreaks a massive havoc to everything that isn't covered. This process takes usually 5-10 seconds, sometimes less.
While mortar blasts have less fragmentation area (75px) when compared to stick grenades (100px) and have a rather large miss zone (of about 150px), the latter actually works to their advantage. Although they must target the nearest unit, they can still hit that far behind it! As such it is highly recommended that you take him out first due to the devastating damage he can do to your trenches full of troops, which is very common to most strategies. It is a good idea to concentrate fire on him to take out the problem fast, or else you will see some American guts flying over your lines.
Snipers may take them down first, but it is best not left to chance. When he tries to deploy his mortar, getting pinned will reset the process, same with firing it, thus giving you advantage when you have a trigger happy Gunner.
In later waves, the German mortar will become pretty accurate so you would have to put it a bit further up on you're priority list.
Given the size of the mortar and the fact it's operated by one person, the Germans are either using the 2 cm leLdgW mortar or the 3,8 cm sLdgW mortar. Both of which were inefficient for their role and were gradually recalled from battle. During the time period this game is set in, there weren't very many still in use.