Firemen who had been battling a fire in a lavishly restored home in Old Town Alexandria yesterday morning discovered the beaten, bound and gagged body of a 38-year-old woman, the member of a prominent Virginia family.

Donita L. Cutts, who had returned from a vacation Friday night, was found in the basement of her home at 125 Wolfe St. almost an hour after firemen began fighting a second-floor fire there. Her body was hidden behind a furnace, firemen said.

No one had looked for her earlier inside the buring two-story town house because some neighbors told firemen Cutts was still on vacation at Rehoboth Beach.

Cutts, who had worked for Goddin Real Estate Inc. in Alexandria until about a month ago, had returned from dinner at Joe Theismann's restaurant in Baileys Crossroads with three friends at about 12:30 a.m., according to other neighbors smelled smoke coming from the 128-year-old house, and called the fire department.

When the fire department arrived after the 5:23 a.m. alarm, flames were coming out of the second-floor windows of the house, located a block from the Potomac River in a neighborhood of restored 19th-century homes.

It took about 30 minutes for firemen to put out the fire on the second floor. Entering the house, firemen found heavy smoke on the first floor coming from the basement.

"It was too heavy to have come just from the second floor," one fireman said. "Obviously someone had set more than one fire in the house. We started clearing smoke out of the basement."

At about 6:15 a.m., one of the firemen discovered Cutts bound and gagged behind a furnace in a puddle of blood.

Police would say only that the fire appears to be of a "suspicious nature." They said they were still seeking a motive and had no suspects.

Friends and neighbors said yesterday they could think of no one who would want to harm Cutts and speculated that she had confronted a burglar who was attempting to steal some of the many antiques she owned.

The Wolfe Street-South Lee Street neighborhood where the house is located is one of restored homes, most of them valued at over $100,000 and many like Cutts' house, filled with valuable items.

Police said yesterday they had not discovered anything missing from the house. Firemen said a recently in stalled burglar alarm had been cut and it seemed "obvious" that at least two fires had been set. Damage to the house and contents was estimated at $20,000.

Police checked around the house and throughout the neighborhood for much of the day seeking clues for a motive. "We still don't have anything." Detective John Turner said yesterday afternoon.

"If she had any enemies like that I didn't know about them," said Wellington Goddin, her former boss. "Dee lived a very social life, knew a lot of people. But I don't know about anything like that."

Cutts, who never married, was the daughter of the late Marine Brig. Gen. Richard M. Cutts and Dorothea Lane Cutts who own a large estate called Dondoric Farm in The Plains, Va. Dorothea is descended from the family of the first governor of Massachusetts and her 1934 wedding to then Lt. Cutts was a major social event in Washington.

Catherine Eldridge, who lives at 123 Wolfe St., said that Donita Cutts had planned to go to the estate this weekend to visit her mother and that was why she had returned from her week-long vacation Friday night.

Goddin said Cutts had left his company about a month ago after working as office manager for about two years because she wanted to invest in land and restore some property.

He said she had recently purchased three pieces of property in Alexandria and planned to restore them. Cutts also owned property near her parents' estate, Goddin said.

Cutts purchased her home in May 1977 from Charles H. Beach, an Alexandria fireman, for $48,000 for the purpose of restoring it. "My family had lived in that house since about the turn of the century," Beach said. "But when my father died it would have taken some work for me to get it in shape to get a good price. She wanted to restore it so I decided to let her take the gamble."

Neighbors said Cutts had finished the restoration recently and often left her door open during the day. "It's just that this is a very quiet, serene neighborhood," one neighbor said. "A lot of us have burglar alarms because we have so much to lose, but no one expects anything violent to happen."

Cutts had lived in the neighborhood eight years, renting what is now the Eldridge house at 123 Wolfe St. and a house at 404 S. Lee St. before buying her house.

Catherine Eldridge said Cutts "entertained frequently, but most of us in this neiggborhood do that. She was an attractive woman. She lived a very social life."