I can see that you're having some trouble with the guy, we all have that one champ who stomps on us all hard too so I can empathize with you. Anywho I think I can at least help you out a bit.
For the most part Morde is heavily countered by mobility, which I'm sure you're already aware of since you pointed it out. Still it can't be understated that mobility hurts him quite a bit as it negates his primary method of lining up reliable q's and passive procs with his e/q/auto combo. Furthermore keeping minions between you and him is a good method of reducing his damage as his q does far more when you're isolated and doesn't chunk until he gets some items.
The real troublemaker when you're fighting him is his passive, if you're playing a melee character it lets him slap your cheeks pretty early on. In general Morde is something like a slightly more forgiving Zed in that unless you can kite him out (not too difficult for heavy cc or fairly mobile champs) he forces you to counter build him to a degree.
is your best friend here. Most of his damage comes in the form of his low cd q and his passive ticks, which the helm effectively counters well.
The ult on the other hand is much more of a sticking point, the counter play for that is vastly different depending on the type of champ you play. If you're a duelist you can always just straight up try to fight him in there, however to do so it is imperative to dodge the e and as many q's as possible to delay the passive from activating quickly. If you're a mage your best bet is to either burst him if possible or chain together your cc and always keep a distance, you're not trying to beat him in the ult so much as just last until it ends,
or
can help you out in the final few seconds you need.
Adc's and anyone else you can use
or
can just bust out straight away since it lets them skip out of the ult entirely.
Other than that he's a juggernaut, he's slow, melee and survivable as all hell. You win by making him come to you and not making it easy by initiating on him when he's still in fighting shape. I'd suggest not starting anything with him when his shield is near full as he's itching to use it for a shield, it's best to wait until he uses it for the heal and then go to town.