Swift is up for six prizes including Best Video and Best Artiste for her edgy single "Look What You Made Me Do", while Mendes follows her closely with five nods, reported MTV.com.
Kendrick Lamar and Ed Sheeran have been nominated in four categories.
Dua Lipa, Julia Michaels, Khalid, Kyle and Rag'n'Bone Man are in the running for Best New Artiste.
In the Best Video nod, Swift faces tough competition from Foo Fighters ("Run), Katy Perry ("Bon Appetit" featuring Migos), Kendrick Lamar ("Humble") and Kyle ("iSpy" featuring Lil Yachty).
Coldplay have been nominated in Best Live and Best Rock.
The EMAs will be held on November 12.