Mar 7:29 For this saying go your way; the devil is gone out of your daughter.
Christ says earlier in Mat 12:37 that by our "words" we are justified and condemned. The term for "words" in that verse and 'sayings" in this verse is the same "logos," which means both "word" and, in a larger sense, our ideas, our way of thinking. Christ says that he came to teach a new way of thinking for us to follow in Mat: 7:24.
When Christ sends people off to live their lives, he often tells them "to go their way" to signify that it is their ideas that determined the course of their lives for example in Mat 8:13.
In Mat 12:27, Christ says that his power to cast out demons from children does not come from false gods who rule over demons, but by his ability to judge the faith of their parents. It is because of that faith that he is able to cure caste out demons. While that faith comes more easily and first through the Jewish tradition, Christ can judge it anywhere.
"Go your way" is from hupagô (hypago), which means "to lead under", "to bring under", "to bring a person before judgment", "to lead on by degrees", "to take away from beneath", "to withdraw", "to go away", "to retire", "to draw off," and "off with you."
"Devils" is daimonion, which means "divinity", "divine power", "a lower divine being," and "evil spirit." Technically, it means "belonging to a demon. ""Evil spirit" is a New Testament usage or interpretation. " It is from daimôn, which actually is the noun "demon." The word 'demon" doesn't necessarily mean "evil" (though it seems the way the Jews used it here), but in Greek is used to refer to a controlling spriritual power, inferior to the gods. It was used to mean "knowing" and "skilled" in the sense that we might say, "He is a demon poker player."