Can the human mind cure a simple mental disorder like depression on its own?

YES!: ... Even when one gets in therapy and feels helped with his/her depression or anxiety, etc, it is one's own mind who did the healing! the therapist & therapy serve merely as a facilitator of such healing... As such, the mind/psyche is its own healer.... We are self healing organisms! thank you for the opportunity to state this ;).

Can certainly help: Cognitive approaches , positive focus/thinking are certainly effective.Some depressions have a definately biological basis(if we don't) have the correct chemical building blocks we will not make the right brain chemistry-the basis of emotion and thinking.