There's not much of Mimnermus left--just one or two longer fragments and a number of shorter ones. But It would be worthwhile for everyone interested in Homer and archaic Greece to read through the main fragments of the lyric, elegiac and iambic poets in Campbell's book:
This book collects most of the important fragments, with helpful notes:http://www.amazon.com/Greek-Lyric-Poetry-BCP-Texts/dp/0862920086/ref=sr_1_1?s=books&ie=UTF8&qid=1395441484&sr=1-1&keywords=campbell+greek+lyric+poetry
There isn't much of this, since for the most part, it's entirely fragmentary, with a few complete poems, and it shouldn't take long to work through the book. Campbell is also responsible for the new Loeb collection, in multiple volumes.
The vocabulary of Greek elegy is essentially the vocabulary of the Homeric poems--and even Tyrtaeus, the Spartan poet, composed elegies in Ionic.