Traveling on a cruise ship from Singapore to Bejing

No.

According to the website of the embassy of Japan in the United States, US citizens do not need a visa for a stay of less than 90 days.

For China, you send your passport (with some other documents) to the Chinese consulate.

Visas for Vietnam means your passport needs to go to the embassy of Vietnam (either by mail, or carried by you in person).

In neither case, you need to send your passport to a different country (unless you want to be technical and consider the embassy/consulate a different country).

Details about the various application processes can be found on the websites of the embassies of the involved countries.

Check with your cruise company and documentation.

Ships, and so cruise passengers have often easier procedures (and it is easier to proof they are short term transit, the rules are old, made for sailors, and it is not really considered immigration).

Additionally, often you doesn't get back your passport when you go visiting the port of call (Note: doesn't forget to have some copies of passport). The ships will send the list of passengers and crew to local authorities. Some time, immigration officer go to the ship to stamp passports, entry and exit, the passports will not leave the ship.

Usually cruise companies cares about visas, and to make it as easier as possible (part of their income is on extras, like official excursion on shores; and they like people go shopping in the city, it helps them to have perks from local authorities).