Who is responsible to do an exit-interview with employee? Manager or HR Business Partner?

Exit interview should be strictly limited  to HR Business Partner or Manager depending upon the level. To have a reliable data from exit interview it is recommended that exit interview is conducted by external consultant. This is totally subject to organisations policy were how seriously organisation takes the Exit Interview data and act on it. 

Either one.. It depends on the company size..Usually it is done by HR manager, but a supervisor or manager could do that !

Thank You

HR not Manager specialty in case if the staff ask for quit