The phrase often implies an unwanted emotion strong enough to change someone's behavior. The dark alley frightened the girl away from taking that route home.
Pro Tip 2/3
Physical Avoidance
It can refer to avoiding physical locations or situations due to fear. Stories of hauntings frightened the tourists away from the old mansion.
Pro Tip 3/3
Context Specific
Use 'frighten away from' in informal contexts where real fear or strong intimidation is involved. The loud noise from the construction site frightened the animals away from their usual feeding grounds.