They go on missions, very frequently outside of America, as a standard part of their early adult life. Learning the local language is pretty much a requirement.
I know that they go on missions. My question was regarding the "Mormon-American" framing which suggests that Mormonism exists in other countries, which I was not aware of.
Very much so, in fact, more Mormons live outside of the US than within the US. The church reports a population of 16,663,663 with 6,592,195 of those living within the US. (got those numbers from Wikipedia).
I live in a small town in Guatemala and the mormon church here is growing very rapidly. According to Google, they're growing at 1.5% annually, which means 255,036 new Mormons every year. However, a church with even a hundred people can heavily sway a small, remote community.
I agree it's not "spreading" per se, but their numbers are respectable among proselytizing religions today. When Islam reached a 1.8% growth rate in the 2000s we were inundated with proclamations that it was the fastest growing religion in the world (eg: https://foreignpolicy.com/2007/05/14/the-list-the-worlds-fas...).
