It is completely unacceptable and unethical to tell a client who is considering suicide to “try it and find out.” I do not know of an instance of that ever happening with any therapist that I personally know or know of.
It is wise to consider seeing a new therapist. The fact that you have suicidal thoughts is concerning and a sign that help is needed. Suicide is never the answer. There are many competent therapists who could help you.
Depression, in the past, was more difficult to treat. Today it is treated with great success. You are going through a difficult period in your life. It is quite common for each of us to have these difficult, troublesome periods. While we are having these painful times in our lives, it is common to assume that they will never end. Please remember that they do end. I have written here before about survivors of suicide attempts. The overwhelming, vast majority are very happy that their attempt failed. They realized the value of life and found the happiness that had been denied them.
I often advise those searching for psychological help to call at least four or five therapists. You want to essentially interview therapists over the phone to find out how they would help you. Discuss your problems and ask specific questions about how they would help. Make an appointment with those with whom you feel the most comfortable. It might take some time to find a good therapist but it is worth your effort. Please take care.