Though the origins of slang words can hardly ever be correctly pinpointed, it is possible that the word "spic", as an insult for those of Hispanic ethnicity, originated as either:

1. An amalgamation of the word "Hispanic" or
2. The pronounciation of the word "speak" with a Spanish accent, where the vowels sound different. The ea sound in "speak" falls closest to the Spanish vowel i, which follows only the short pronunciation of such letter in English (as in the word "spic"). The word "speak", being used often in such simple sentences as "I don't speak English", may have been mispronounced enough times by Spanish speakers as to be converted into the derogatory word "spic" by English speakers.