1) The question of "visa-free" nowadays usually ONLY RELATE to entry into a country by FOREIGN NATIONALS. (Thus- in the present context- it should be focused on visa-free access by NON-CHINESE nationals)
2) Those who hold the HKSAR passport, Home permit (or mainland travel permit), other Chinese passports, etc., that is, all those who possess Chinese nationality, do not fall within the scope of the question of visa-free access.
3) China (mainland) grants visa-free access to the citizens of a number of countries, e.g. SIngapore, japan., and especially those who hold a diplomatic or official passport. You may see
www.fmprc.gov.cn for more details