A word with a silent "m," such as "mnemonic," as well as any word with a silent letter, is typically that way because it was derived from another language; or, the silent letter was once pronounced, but usage changed and the spelling did not. The prefix "mnem-" comes from Greek and means "mind." Greek words such as "gnostic," "pneumonia" and "psychiatry" begin with clustered consonants that are unpronounceable in English, so usage dictates the first letter is silent.
The "mn" letter combination appears in other words where the letter "m" is pronounced, such as "hymnal" or "amnesia." There are other words that end in "mn," such as "autumn," "column" and "condemn," for which the "m" is pronounced but the "n" is silent. In Latin and Greek, these words typically had suffixes following the "mn" consonant clusters, but over the centuries as the English language evolved, the suffixes dropped off, leaving a difficult-to-pronounce letter combination, so the "n" became silent.
Until the 15th century, 90 percent of English words were pronounced exactly as they were spelled. As Europeans began to travel, words from other languages were introduced into English. These new words did not follow the same rules of grammar and pronunciation as English, so although the spelling stayed the same, some letters became silent. Language experts estimate that as of 2015, 60 percent of words in English have at least one silent letter.