Quoting John Scanlon <riversleigh@outbackatisa.com.au>:
Because the idea of 'extinction' in anything like the modern sense is relatively young (Cuvier?) there is probably not a snappy, authentically classical Greek word to use. But why not Modern? Going to http://www.translatum.gr/ (only the first free online translation site I found) and typing in 'extinction' gets a word I transliterate as 'exaleipse' (extinction of a race = exaleipse phyles), so what you're looking for would be exaleipsology.
-- Nick Pharris Department of Linguistics University of Michigan
"Creativity is the sudden cessation of stupidity." --Edwin H. Land