No, it doesn't make any sense in Danish.
I would rather say one of the following, depending on the context:
"Du kender mig for godt" = "You know me too well."
"Lige mine tanker!" = "My thoughts exactly!"
What about literally reading someone's thoughts (like some superheroes might telepathically read someone's mind)? Of course it's a fictional situation that wouldn't really come up in conversation, but I'm just curious
That would be "Du læser mine tanker." A mind-reader is called "en tankelæser".
"sind" is closer to soul, temper or mentality.
EDIT: You can say "Du læser mit sind", but it means "You read my temper" or "You read my soul"