The only description I can find of his power is on BS01, where it says "Mimic has photographic reflexes; if he watches a being doing any kind of physical feat, he can replicate it, perfectly, instantly, and without practice." It also mentions that he carries a weapon/tool in order to be able to mimic actions that make use of such tool.
Reading this I don't think he can copy special powers or other traits such as raw body strength. "Photographic reflexes" means he can go through the motions of any action he witnesses, so he could mimic your swordplay to parry your attacks perfectly, or he could let you scale a cliff with your years of rock climbing experience and then mimic your actions to follow you to the top without having to learn the skill himself.
If he saw Pohatu kick a rock into the sky, however, he probably would not be able to get the rock to fly as far, even if he copied the motion itself perfectly. I also don't think he could copy actions that require an entirely different body shape - if he watched a snake moving smoothly across a surface he would gain an intuitive understanding of how to accomplish the task, but he could not actually do it because he is not a snake.
The mimicked Sonic Scream you propose would probably be identical in how it sounds, but if measured in decibels it would not come anywhere close to the intensity of the amplified sound wave created by the actual Sonic Scream power.
There are other abilities that allow you to change yourself or copy special powers - such as Shapeshifting, the Adaptation Kraata power and Reidak's power, the Mask of Emulation and Krahka's power - which implies to me that Mimic is meant to be doing something else.