Mumbled adverbs are provided in this article. The words listed here are commonly found along with the verb mumbled in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb MUMBLED.
finally
incoherently
quietly
sleepily
softly
Hope this word list had the mumbled adverb you were looking for. In addition to adverbs used with mumbled, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.