Recently I finished my Masters. My relationship with my thesis supervisor is very bad. He is a professor. I am very disappointed with his mentoring. He is very lazy and always kept himself busy with work other than research. I expressed my dissatisfaction to him directly. That made him furious at me. I have planned to pursue my Masters degree at a university in North America. Three reference letters are required. I don't want my thesis supervisor as a referee. Other faculty members in our department have agreed to refer me. But will it affect my admissions chances negatively if I don't submit a reference letter from my thesis supervisor?
It will look a bit weird, yes. And the other faculty members in your department probably do not know you as well as your thesis supervisor, so their letters of recommendation will not be very specific. But I've never seen this be reason for an immediate rejection, which means you can make up for it in the rest of your application.
Probably an unnecessary tip, but: don't express your dissatisfaction with your supervisor in your applications.