Can an American travel to the Philippines on a foreign Visa without vaccine?

Americans DO NOT NEED A VISA to travel to Philippines.

 Philippines Visa not required[382][383] 30 days

Naturalized US citizens of former Philippine nationality (balikbayan) allowed to stay for one year.

What do you mean by a "foreign visa"? Your passport establishes your nationality. The COVID rules in most countries have to do with the physical places people are coming from, not their nationality. A few places are starting to open up to people who have been vaccinated. If you want to travel, GET THE VACCINE! I'm betting you're looking at YouTube videos and believing the nonsense in them instead of believing the thousands of scientists who say that it's safe to get the vaccine, and it will protect you and other people. People who aren't getting vaccinated are incredibly selfish- they are stopping the rest of us from being able to go back to normal. As long as there are many cases per day, things will continue to stay closed. GET THE VACCINE! Come to my state when anyone over 16 can get it just by walking in. 

There are different rules depending on the country and nature of travel, i.e., business or pleasure.  The best thing to do is goole "phillipines covid" and go to the government website for all the rules.  At the very least, you probably need a negative covid test within 72 hours of arrival.