I will do anything that would harm my mind.

will引导句子后面要加虚拟语气
即will+that+would(should)+do

would表示虚拟语气。
用过去式表示。

这是高二将要学的虚拟句的用法
虚拟句中的从句都要用过去式或完成式来表达
If I were you,I would give him a gift.