I have two passports. One is Hong Kong (HKSAR)passport. One is British Citizen passport (GBR). For both passports, they are visa exempted to enter to Japan. My question is last month I used the British passport to go to Japan. I am going to Japan in next two weeks and I want to use the Hong Kong passport. Is it okay?
Totally fine. As long as you enter and exit the destination country on the same passport, it's acceptable.
There are some rules for citizens returning to their country, eg American citizens are obliged to enter the US on their American passport, but generally, as long as you arrive/exit using the same passport (And it doesn't have to be the same as last time - you might have changed citizenship in that time!), you'll be fine.