Old English slim "slime," from Proto-Germanic *slimaz (source also of Old Norse slim, Old Frisian slym, Dutch slijm "slime, phlegm," German Schleim "slime"), probably related to Old English lim "birdlime; sticky substance," from PIE root *(s)lei- "slimy, sticky, slippery" (source also of Sanskrit linati "sticks, stays, adheres to; slips into, disappears;" Russian slimak "snail;" Old Church Slavonic slina "spittle;" Old Irish sligim "to smear," leinam "I follow," literally "I stick to;" Welsh llyfn "smooth;" Greek leimax "snail," limne "marsh, pool, lake," alinein "to anoint, besmear;" Latin limus "slime, mud, mire," linere "to daub, besmear, rub out, erase"). As an insult to a person from mid-15c. Slime-mold is from 1880.
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