Mr Stephenson said: “Our thoughts are with Matthias’ family.
“It doesn’t take a lot of thought to imagine how horrible it must be to have somebody missing for some amount of time. This is obviously terrible news.”
Mr Stephenson said it had been “frustrating” that they had not found Mr Beutin’s body sooner.
But he added the team were glad to be able to “bring him home” and allow his family to start the grieving process.
He said the search had been hampered by testing conditions.
“It’s very difficult terrain to search in difficult weather and there are acres and acres of ground you can’t easily access,” Mr Stephenson added.
Helicopters and drones only had a limited role in the search but a break in the weather on Saturday gave the team an opportunity to resume their efforts.
Skye Mountain Rescue were joined in their search by Kintail Mountain Rescue, Glen Elg Mountain Rescue, members of the Police Scotland Mountain Rescue team and the Rescue helicopter.
The Search and Rescue Dog Association and the Royal Air Force Mountain Rescue Service had taken parts in previous efforts to find Mr Beutin.
Blà Bheinn, also known as Blaven, is a popular Munro for walkers and climbers in an isolated part of Skye, on the outskirts of the Cullin Ridge.