Frank S., 44, has been in police custody since he was arrested at the scene of the assault on the eve of Henriette Reker's election in October.
The unemployed house painter stands accused of attempted murder and causing grievous bodily harm.
At the opening of his trial, the defendant pledged to tell the court in Düsseldorf about his motives.
He detailed his participation in the right-wing scene in Bonn in the 1990s and described himself as a "rebel with conservative values," but denied being a Nazi.
Prosecutors say the bloody attack was motivated by his opposition to what he deemed the "wrong policy" of Chancellor Angela Merkel's government to take in large numbers of refugees.
Reker, who was previously in charge of running refugee services in Cologne, was attacked while she was campaigning at a market square.
She subsequently won the local elections while recovering from her wounds in hospital.
The assault shocked Germany at a time of growing division over the government's decision to open its doors to people fleeing war and misery, with more than one million arrivals last year alone.