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.