싹다갈아 should be written as 싹 다 갈아. It's an adverbial phrase for "changing everything completely".
* 싹 = Onomatopoeic adverb describing an action of doing something completely and decisively.
* 다 = completely, all.
* 갈아 = 갈다(change, replace) + -아(verb ending for connective "and') => (by/through) changing, or a command to change.
싹다갈아 나로 사는게 (-> 싹 다 갈아. 나로 사는 게 ...) looks like one complete sentence (싹 다 갈아) followed by another incomplete one.
I checked and saw some lyric page that breaks up the lines this way (maybe it's following the song's structure).
If you go by the sentential structure, it should be like this.
싹 다 갈아 => Change everything completely.
나로 사는 게 싫어 => I hate to be living as me.
믹서기로 => With a mixer,
머리부터 발끝까지 다른 사람이 되기를 빌어 => I pray to be a different person from head to toe.