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.
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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."
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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.