The star won four trophies, including artist of the year, making her the ceremony's most-decorated female ever.
She now holds 23 AMAs, beating a record previously held by Whitney Houston.
Swift, who recently broke years of political silence to declare support for two Democrats, again urged fans to take part in the US mid-term elections.
Accepting artist of the year, she said: "This award, and every single award given out tonight, were voted on by the people.
"And you know what else is voted on by the people? The midterm elections on November 6. Get out and vote. I love you guys."
Swift's touring partner Camila Cabello also won four awards at the ceremony; while British singers Ella Mai and Dua Lipa gave show-stopping performances.