Blue's Clues cut episode's beginning and ran wild (8)
I believe the answer is:
cerulean
'blue's' is the definition.
(cerulean is a kind of blue)
'clues cut episode's beginning and ran wild' is the wordplay.
'cut' means to remove the last letter.
'beginning' indicates taking the first letters.
'and' is a charade indicator (letters next to each other).
'wild' indicates an anagram.
The initial letter of 'episodes' is 'e'.
'clues' with its final letter removed is 'clue'.
'clue'+'e'+'ran'='clueeran'
'clueeran' with letters rearranged gives 'CERULEAN'.
(Other definitions for cerulean that I've seen before include "Light shade of blue" , "Sky-blue for Laurence" , "of clear heavenly appearance" , "Deep blue colour" , "Sky-blue in literary way" .)