Why can't I use 我的 in Classical Chinese? almost all words are stand alone in classical texts. Only modern Chinese tend to use multi characters to form a word.  Your examples would be 明身/明体， 明心. But  明我的心 is not a traditional way.

Why can't 心 be modified with a adjective in Classical Chinese??
Why can't 心 be modified with a adjective in Classical Chinese?


Of course it can. In your case, 明吾心、明吾之心、明我心、明我之心 are all correct. 

"的" is not common in classical texts, you can use "之" instead or just omit it.