Correct spelling, explanation: the word consists of two elements, the noun speech and the suffix less. It is an adjective that was used in Middle English as specheles but it is one of the oldest words already known in Old English. As we see, the word is slightly changed but it can be confused with the verb speak that existed in Old English as sprecan, very similar to modern German sprechen. But the spr forms were extinct in English by mid 12th century. To sum up, speechless is made from speech, not from speak, therefore only speechless is correct.

Definition of speechless:
adjective, when someone is speechless, he is surprised or angry that he or she is unable to say words with an ordinary voice.
When Gabriel saw her, he was speechless for a long moment.
Although I had been prepared for the worst, her story left me speechless.
The price of this hat made her speechless.

Incorrect spelling, explanation: it is a common mistake that people make because they confuse the noun speech with the verb speak. But speech conveys the meaning of an act of verbal communication, whereas speak to communicate. As we can notice, these words are different. As an adjective speechless is formed from the noun speech, not the verb speak and the users of English should memorize that speachless is incorrect and need to spell this word as speechless.

Incorrect spelling

Incorrect spelling

Incorrect spelling