
Give someone the kiss-off
Give someone one's running shoes / Dump someone (Slang) / Give someone the gate

Dare il benservito (relazione) 
Give someone one's running shoes / Dump someone (Slang) / Give someone the gate

Dare il benservito (relazione) 
Meanings
Fig.: to break up a relationship for good
Examples
Renzo thought he could afford to do anything he wanted because his girlfriend was a shy and indulgent young girl, but as soon as she met a more decent guy, she gave Renzo the kiss-off without even thinking about it twice
Renzo pensava di potersi permettere tutto perché la fidanzata era una
giovane timida e accondiscendente, ma non appena lei ha conosciuto un
ragazzo più serio, gli ha dato il benservito senza tante storie