The couple's bodies were pulled into the grass on the side of the road, leaving police to initially think they were hit-and-run victims.
However, investigators said both victims were stabbed multiple times, and their throats were cut, WFTV reported.
Police do not believe the attack was a robbery.
"We can't rule out that this may be totally random," Daytona Beach Police Chief Jakari Young said. "But if it is totally random, the person responsible has to be deranged."
The stabbing happened around 1 a.m. Sunday. Neighbors told police they didn't hear or see anything.
Police said they are looking for a man they believe was wearing light-colored or white pants and a backpack.
Investigators are reviewing security video in the area to help them develop more leads.