Can mainland residents travel to Macau or Hong Kong with a Taiwan Travel Permit?

You can, but there are risks. It is recommended not to do this.

Using this document to enter Hong Kong and Macau can stay for 7 days. This is of course no problem.

But If you have not arrived in Taiwan, when you leave the country from Hong Kong or Macau and return to the mainland, you will be asked to fill in the place of entry into Hong Kong on the exit form. Your entry information will be checked, and then the person entering and leaving the country will also ask you why you did not leave the country. You have to do this What a good excuse to answer.

A friend tried it before and was questioned for a long time. Her itinerary for those days was also checked. After a round of procedures, she was finally allowed to return to the mainland. And she was also warned, You will be detained if you do this.

Anyway, this document is only for transit to Hong Kong and Macau, and there is still a difference between it and the Hong Kong and Macau Pass.