Is it possible to get infected by using a nail cutter that has been used by an HIV infected Person?
No need to worry - HIV is very fragile and lives outside the body for a very short time. The only way that a nail cutter may be any threat would be if there is fresh blood on it from an HIV infected person and then you were cut and the blood entered your bloodstream. And even that is a very minor risk since there would likely not be enough virus present unless a lot of blood was involved.
The best idea is just to make sure that the nail cutter is clean.