Mulesed is recognized by a few dictionaries, including the Shorter Oxford, Wiktionary and the Macquarie.
The Mules operation is named for J H W Mules, the South Australian who devised the procedure. From that we get mulesing as a noun, mules as a verb and mulesed as an adjective. These words, and presumably the operation, are mainly used in Australia. Use of the word in other countries is usually in connection with efforts by animal welfare groups to promote boycotts of Australian wool, alleging that mulesing causes unnecessary pain to the sheep.
Mulesed and mulesing certainly qualify to be admitted as rare words. The third person present tense, logically, is the awkward muleses, and so some dictionaries specify. I couldn't actually spot any instances in live usage, but for consistency I'll add that also as a rare word.
