They aren't two different words that have the exact same meaning, in fact "uttermost" is just another word for "utmost" and the only difference I see is the different prefixes "ut" and "utter". So conclusively these two words are in fact clones.

How do you use uttermost in a sentence?

Officers and men alike will put forth their uttermost strength. There are four-and-a-half million Norwegians, clinging to an icy strip of tundra on the uttermost edge of the continent. Whereof fail you not as you will answer the contrary at your uttermost perils '.

What means uttermost?

1 : outermost. 2 : extreme, utmost. uttermost.