Process for manufacturing tyres for vehicle wheels, comprising: - forming components of a green tyre on a forming drum, - shaping, moulding and vulcanising the tyre; wherein forming at least one of the components of the green tyre comprises: supplying an elongated element made of elastomeric material along a feed path, wherein the elongated element is longitudinally extended along said feed path; cutting a piece from a head section of the elongated element; advancing the piece on a conveyor up to a forming drum; depositing said piece on a surface radially outer with respect to the forming drum; wherein cutting comprises: depositing, between an abutment surface and a coupling surface (42, 46) that are opposite each other, each of two portions (T, H) of the elongated element situated on opposite sides of a transverse cutting line in order to oppose, substantially preventing, a movement of the elongated element with respect to said abutment surface and/or said coupling surface (42, 46); cutting the elongated element along said transverse cutting line while said two portions (T, H) are arranged between said abutment surface and said coupling surface (42, 46); after the cutting, retaining each of said two portions (T, H) on the respective coupling surface (42, 46) and moving said coupling surfaces (42, 46) and said portions (T, H) associated therewith towards the conveyor; wherein said coupling surfaces (42, 46) are moved together towards the conveyor. - forming components of a green tyre on a forming drum, - shaping, moulding and vulcanising the tyre; supplying an elongated element made of elastomeric material along a feed path, wherein the elongated element is longitudinally extended along said feed path; cutting a piece from a head section of the elongated element; advancing the piece on a conveyor up to a forming drum; depositing said piece on a surface radially outer with respect to the forming drum; wherein cutting comprises: depositing, between an abutment surface and a coupling surface (42, 46) that are opposite each other, each of two portions (T, H) of the elongated element situated on opposite sides of a transverse cutting line in order to oppose, substantially preventing, a movement of the elongated element with respect to said abutment surface and/or said coupling surface (42, 46); cutting the elongated element along said transverse cutting line while said two portions (T, H) are arranged between said abutment surface and said coupling surface (42, 46); after the cutting, retaining each of said two portions (T, H) on the respective coupling surface (42, 46) and moving said coupling surfaces (42, 46) and said portions (T, H) associated therewith towards the conveyor; wherein said coupling surfaces (42, 46) are moved together towards the conveyor. depositing, between an abutment surface and a coupling surface (42, 46) that are opposite each other, each of two portions (T, H) of the elongated element situated on opposite sides of a transverse cutting line in order to oppose, substantially preventing, a movement of the elongated element with respect to said abutment surface and/or said coupling surface (42, 46); cutting the elongated element along said transverse cutting line while said two portions (T, H) are arranged between said abutment surface and said coupling surface (42, 46); after the cutting, retaining each of said two portions (T, H) on the respective coupling surface (42, 46) and moving said coupling surfaces (42, 46) and said portions (T, H) associated therewith towards the conveyor; wherein said coupling surfaces (42, 46) are moved together towards the conveyor.