Jeremy Joseph Christian, 35, did not enter a plea during his brief arraignment on charges including two counts of aggravated murder, which carry the death penalty.
"Get out if you don't like free speech" and "You call it terrorism, I call it patriotism. You hear me? Die," he shouted in the courtroom, flanked by two deputies.
"Death to the enemies of America. Leave this country if you hate our freedom," he added.
Christian is due back in court on June 7.
Attending the hearing on Tuesday was Micah Fletcher, who was wounded as he tried to defend a black 16-year-old and her Muslim friend as they rode on a crowded train on Friday.
Christian allegedly targeted the teens, one of whom wore a hijab, with racial and religious insults.
Two other men who tried to intervene were fatally stabbed.
Fletcher told the local NBC station on Tuesday that he was trying to come to terms with the tragedy.
"I got stabbed in the neck on my way to work, randomly, by a stranger I don't know, for trying to just be a nice person," said the 21-year-old university student. "Like, I don't know what to do after that, you know.
"I'm healing. That's what I'm doing. As much as I can, in whatever way I can."
According to reports, Christian was a known white supremacist and had appeared at an "alt-right" rally in Oregon in April during which he had yelled racist slurs while giving a Nazi salute.
He was also previously convicted for robbery, kidnapping and weapons-related charges, according to media reports.
One of the teenage girls targeted by Christian said she was with a friend who was wearing a hijab when he approached them and began hurling abuse.
"He told us to go back to Saudi Arabia, and he told us we shouldn't be here, to get out of his country," Destinee Mangum told KPTV.
"He was just telling us that we basically weren't anything and that we should kill ourselves."
President Donald Trump described the attack as "unacceptable" in a tweet on Monday.
