It appears that deed (n.) is not much related to dead:
Old English dæd "a doing, act, action, transaction, event," from Proto-Germanic *dædis (cognates: Old Saxon dad, Old Norse dað, Old Frisian dede, Middle Dutch daet, Dutch daad, Old High German tat, German Tat "deed," Gothic gadeþs "a putting, placing"), from PIE *dhetis (cognates: Lithuanian detis "load, burden," Greek thesis "a placing, setting"), from *dhe- "place, put" (see do). Sense of "written legal document" is early 14c. As a verb, 1806, American English Related: Deeded; deeding.
while mortgage (n.) has some relation to it:
late 14c., morgage, "conveyance of property as security for a loan or agreement," from Old French morgage (13c.), mort gaige, literally "dead pledge" (replaced in modern Frech by hypothèque), from mort "dead" (see mortal (adj.)) + gage "pledge" (see wage (n.)). *So called because the deal dies either when the debt is paid or when payment fails. Old French mort is from Vulgar Latin mortus "dead," from Latin mortuus, past participle of mori "to die" (see mortal (adj.)). The -t- restored in English based on Latin.
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