Hilary attempted suicide over the weekend, and died Monday in a hospital, according to sources with direct knowledge. The Giants honcho mourned his daughter's death in a statement to TMZ ... remembering her as "a kind, caring and beautiful person."

Steve adds ... Hilary's "mother, sisters, brothers and I are devastated by her passing. It leaves a hole in our hearts and our lives. She, like so many others, bravely fought the disease of depression for as long as she could."

Our sources say Hilary, a successful jewelry designer, had struggled through depression for many years. Despite that, she poured her heart and soul into volunteering with Operation Smile, a nonprofit medical service organization that's provided over 220,000 free surgeries around the world for kids and young adults born with cleft lips, cleft palates and other facial deformities.

Hilary's father says the Tisch "family is utterly heartbroken and is mourning its tragic loss. We love and will miss her dearly."

Hilary was 36.