Ellen Higginbottom's body was found at Orrell Water Park, Wigan early on Saturday - a Wigan man, 47, and a man, 51, from Preston are being questioned.
Post-mortem tests found Ellen, who was reported missing on Friday, died due to "multiple wounds to the neck".
Louise Tipping - principal at Winstanley College, where she studied - said: "Ellen was absolutely wonderful."
She added: "Her contribution to our college was fantastic."
Ms Tipping said she had received many emails over the weekend from students asking how the college would pay tribute to the girl who was a student ambassador at the college.
She added: "Ellen was much loved. She was one of those people who lit up the room. She was a lovely, lovely girl."
Ellen was reported missing after failing to return from college.
Friends said she was last seen in the Orrell Water Park area.
Police found her body at about 02:30 BST on Saturday during a search.
A 47-year-old man from Billinge, Wigan was arrested followed by a second man who was arrested at an address in Preston.
Police said his address was being searched and there was a large police presence in the area.
Det Supt Howard Millington from Greater Manchester Police said: "It is unimaginable what Ellen's family and friends must be going through right now and my thoughts continue to be with them throughout all of this.
He added: "Whilst we have now made two arrests, our investigation continues as we piece together the puzzle to find out what exactly happened to Ellen on Friday and give her family the answers they deserve."
Floral tributes for the popular Wigan student have been laid at the scene.
A second man has been arrested on suspicion of murdering an 18-year-old student found dead at a beauty spot.