Vonn has faced hostility from some supporters of U.S. President Donald Trump since she said in December that she would not visit the White House if she won an Olympic gold medal.
The 33-year-old also said that she was representing "the people of the United States, not the President" at Pyeongchang.
Vonn's failure to medal in her opening event, the Super-G on Saturday, prompted some social media users to mock her performance, celebrate her failure and express hopes of her injuring herself.
"That is what bullies want you to do. They want to defeat you and I am not defeated, I am the same," she told reporters after training for Wednesday's downhill.
"I stand by my values and I am not going to back down. I may not be as vocal right now with my opinions but that doesn't mean they have won – I haven't changed my mind."
Vonn said some of the comments had affected her, but she had decided not to monitor social media before her races.
"It is hard. Definitely before the race I don't go on social media, I may post something but I don't look at anything," she said.
"I always try to remember that is people talking behind a computer and they are going to say anything and the most important thing is that I am having a good time, I am enjoying being at the Olympics, my family is here, they love me.
"There are of course going to be people who hate me and hope I ski off a cliff and die. That's fine – I'm not going to do that.
"I just take it for what it is, at some point you just have to laugh and say it is completely ridiculous."
(Editing by Greg Stutchbury)
