# a Canaanite woman came out from that region

“a woman who was from that region and who belonged to the group of people called Canaanites came.”

# Have mercy on me

"Have mercy and heal my daughter" 

# Son of David

"Son of David" is also a title for the Messiah, and the woman may have been calling Jesus by this title.

# My daughter is severely demon-possessed

"A demon is controlling my daughter terribly" or "A demon is tormenting my daughter severely"