She then sped across the city and even managed to arrive at North Manchester General Hospital before ambulance services.
Twenty two people were murdered and 119 injured when suicide bomber Salman Abedi detonated explosives at the Ariana Grande concert.
Recalling the terrifying night, Mrs Shutt said : "I knew he [Gary] was bleeding to death. I thought it was a nail bomb just because of the nails and screws in his wounds.
"We put my daughter in a taxi down the road with her dad and my husband.
"What I did just came naturally. I didn't really stop and think. I just wanted to help.
Trained nurse Lianna Shutt was leaving Manchester Arena with her family when she spotted a severely injured man with his daughter. Photo / Facebook
"I had to make the devastating call to Gary's wife that her husband had sustained traumatic injuries and that I was looking after their daughter.
"I drove at 100mph to get them to hospital and I was weaving in and out of cars. The police have told me they will cancel all my speeding tickets as it was a matter of life and death to get him there as quickly as possible.
'I got him to North Manchester hospital and the surgeon came up to me outside and said I was the first person to arrive. Even the ambulances hasn't got there with casualties. He said I had saved his life.'
Mrs Shutt had been at the pop concert with her 10-year-old daughter Broganjean Taylor and husband Martin Shutt.
She said "incredibly brave" Gary had helped save his daughter's life by shielding her from the explosion.
Police escort members of the public from the Manchester Arena after a suicide bomber killed 22 people. Photo / Getty
The father, from Birmingham, has now been transferred to Queen Elizabeth Hospital in his home city and told Mrs Shutt that "thank you will never be enough".
She said: "Gary had saved his daughter's life. He put himself over her and covered her from the blast.
"He was so calm. To have all those injuries and being in the back of my car, you would expect somebody like that to be screaming in pain.
"I went back to hospital to see him on Thursday. His wife phoned and asked if I could. He's doing well.
"He told me that he wasn't going to say thank you because it would never be enough.
"He's been trying to put the jigsaw of what happened back together. He said when he can find something to thank me he will do but I said it wasn't necessary."
Mrs Shutt said her daughter had been in Alder Hey Children's Hospital in Liverpool for the last nine weeks with a 'life-threatening' sespsis infection and was only given permission to go to the concert two hours before it started.
Broganjean was knocked out of her wheelchair at the arena due to the force of the explosion, but thankfully didn't suffer any injuries.
Mrs Shutt said: "She has been waiting 18 months to go to the concert since we realised Arianna was coming to the UK on tour.
"She has been in hospital for nine weeks. The doctors knew if she didn't go she would be heartbroken.
"She has rheumatoid arthritis and was in hospital for a planned visit but then got sepsis. It was life-threatening.
"We were sat near the merchandising block where the explosion happened. The force of the blast blew my daughter out of her chair. Thankfully she wasn't injured but she is traumatised by what's happened."
The people of Manchester mourn after 22 people were killed in the blast. Photo / Getty
After initially treating Gary at the scene, Mrs Shutt said she then helped another girl, believed to be 15, who had suffered shrapnel injuries to her leg.
She is desperate to find out what happened the victim after she handed over treatment to doctors.
The former nurse said: "I think she was 15 years old and was call either Ali or Millie.
"I had stopped the bleeding, applied pressure and bandages to the wound in a few places and made sure she had a pulse to her leg.
"I had to hand her over to two junior doctors when I went with Gary to the hospital. I would love to know what happened to her and to know that she is okay."
