I see a lot of folks saying that new Morde is OP. He is strong, but honestly, it's not that hard to beat him.
I downloaded pbe just to practice him some before he hit live, and here is my take:
If an enemy picks Mord, I pick Aatrox. With the knockups on Troxxi's Q, you can keep Morde at a distance, thus denying his passive damaging you very much.
Oh, Morde pulled you? Use Aatrox's E to dash away and out of his passive. Morde's Q has 60% AP ratio, which is the same value as his last e, which isn't a lot.
Also, Morde has an awful heal now, so he can't just heal back to full hp like last Mord can. Also, his sheild has a CD now, since it is his w, so the "always sheild, never die" meme is dead.
As Aatrox against Mord, you simply poke at a decent range with Q, keeping him in line by hitting him with your sweet spots. If you use these knockups to cancel Morde's animations, the Morde won't be able to do much other than get rekt.
Beware of his passive! When Morde's DoT passive is up, GTFO away, knock his ass up, and wait for his passive to go away to get closer to him. Grab boots early to kite him.
Also, try to save your ult till after Morde ults you. Yes, he may steal 10% of your base stats, but just use Aatrox's ult to outstat the Mord. Not only will you have more damage than the Morde who just ulted you, but between your ult and Conq, you will hesl for MUCH more than him, because remember, his heal on W is trash now, and his defensive stats were hotfixes nerfed.
Honorable mentions of escapes from Morde ult:
Cleanse if used during his channel.
Olaf can ult out of Death Realm.
Fiora can Parry his ult.
You can QSS his ult away, even while inside it.
Malz can use his ult to cancel Morde's or keep him still in Death Realm
WW can do the same.
Sivir can Spell Sheild.
Morganas Spell Sheild also blocks Morde ult.
Edge of Night active negates Morde's ult as well.
TL;DR: Pick a champ that can poke at a distance with some usefull cc. Buy a QSS against Mord to make him never able to use his ult.