That prisoner was reported ____(abuse)many times and later he died

to have been abused many times and later he died
在已经被虐待了多次后死了.

死之前已经被虐待了,be reported to have done sth
被报道已经被...

你的老师是正确的
be reported to do是基本结构，而abuse根据后面的many times我们知道是完成时的时间状语，所以用to have done,又因为是表被动，所以最终答案便是你老师说的那个了。

be reported to
由于abuse 这一动作已经发生过很多次切动作以完成，