The clues can each be solved with two-word phrases, with one letter changed between each pair. These pairs can be assembled into a word chain that branches once:
Took one turn at darts -- THREW THREE
Tossed an ill-tempered woman - THREW SHREW
Scatter a mole-like mammal - STREW SHREW
Disseminate plague - STREW STREP
Soak throat bacteria - STEEP STREP
Cliffside nap - STEEP SLEEP
Alarm clock chime - SLEEP BLEEP
Censorship going too far, perhaps - BLEEP BLEED
Transfusion result - BLEED BLEND
(branch 1)
Barbie/Ken offspring, genetically - BLOND BLEND
Jeff Healey, e.g. - BLIND BLOND
(branch 2)
Flavorless signature coffee - BLAND BLEND
Milquetoast shutout - BLAND BLANK
The unused ends of the chain are THREE, BLIND, and BLANK, thus the answer is MICE.