1590s, "destroy the clarity of" (a transferred sense); literal sense ("to bathe in mud") is from c. 1600; perhaps frequentative formation from mud, or from Dutch moddelen "to make (water) muddy," from the same Proto-Germanic source. Sense of "to make muddy" is from 1670s; that of "make confused, bewilder" is recorded by 1680s. Meaning "to bungle" is from 1885. Related: Muddled; muddling.
"soft mixture, mass of ingredients beaten or stirred together," late Old English *masc (in masc-wyrt "mash-wort, infused malt"), from Proto-Germanic *maisk- (source also of Swedish mäsk "grains for pigs," German Maisch "crushed grapes, infused malt," Old English meox "dung, filth"), possibly from PIE root *meik- "to mix."
Originally a word in brewing; general sense of "anything reduced to a soft pulpy consistency" is recorded from 1590s, as is the figurative sense "confused mixture, muddle." Short for mashed potatoes it is attested from 1904.