Americans don't all use "carmel". Many of them think it's more correct to say "carr-a-mel", so you can find a number of examples of this pronunciation being used, especially in formal contexts. Go through some of the Youglish US pronunciations of "caramel".
I do know however of one word where a similar syncopated pronunciation is, as far as I know, universal for American English speakers: squirrel.
Phonetically, it may actually be one syllable or two, probably in part due to uncertain syllabification of word-final /l/ after /r/. But the identity of the rhotic vowel (/ɜr/ as in "fur" rather than /ɪr/ as in "mirror") points to this word having been underlyingly compressed to one syllable in the historical ancestor of the pronunciation that modern American English speakers use.
I don't know of any other examples besides these two, though. (Unless you count iron = iern, which occurs also in British English, and the less common irony = ierny.)
I don't know what caused these pronunciations to be established only in North America. It seems possible that the presence of rhotic vowels somehow contributed; in most British accents it would be impossible to have "r" in words like /kɑrməl/ or /sqɜrl/, since "r" at the end of syllables has been converted to mere alteration of the length or quality of the preceding vowel (i.e. we'd have to have something like /kɑːməl/ or /sqɜːl/).