This is clearly a very stressful situation for you and particularly for your mother.
Your mother has been through a lot and all this stress may have led to her feeling depressed. When you have written that 'my mom is depress', can you confirm that her current behavior is very different from what it was before she was diagnosed with cancer?
Also, breathlessness can be quite scary, and I can understand why your mother is scared of it.
These are some things you could do -
1. Consult a psychiatrist
and, if indicated, start her on medications and/or psychotherapy
for her depression
2. Reassure your mother that the tube will be removed only after she is completely ok with removing it.
3. Try to take the focus away from the tube. I know you are worried regarding the tube, but consciously make an effort to try and speak with your mother about other things. Discuss with her how she is feeling. She will feel better once she feels understood by her loved ones.
If you follow this advice and your mother feels more relaxed, you may check again if the tube can be removed. Remember though, that the problem regarding the tube may not be entirely psychological. She did turn purple in the hospital and that is pretty serious. But at least you will know for sure whether it is her fear/anxiety
that is causing the trouble, or if there is something else.
Hope this helps, and all the best.