Process for building tyres for vehicle wheels, comprising: forming at least one component of the tyre on a forming drum, wherein said component is formed by means of: supplying a continuous rubber-covered belt; cutting to size said continuous rubber-covered belt; laying the continuous rubber-covered belt, cut to size, on the forming drum; wherein cutting to size comprises: ▪ carrying a knife formed by a first half-part and by a second half-part above the continuous rubber-covered belt, in proximity to a central portion of a cutting zone; ▪ lifting a lifting element placed below the continuous rubber-covered belt and at the cutting zone, until a portion of rubber-covered belt is lifted; ▪ lowering the single first half-part of the knife, making it slide with respect to the second half-part, until it obtains an opening in said rubber-covered belt and inserting the first half-part in the aforesaid opening; ▪ jointly moving the first half-part and the second half-part along a cutting direction and in a cutting sense for generating a notch in the rubber-covered belt by means of said first half-part; ▪ lowering the second half-part, making it slide with respect to the first half-part until said second half-part is inserted in said notch; ▪ symmetrically moving said first and second half-part (46, 50) synchronously away from each other, in opposite senses and along said cutting direction; wherein cutting comprises forming, with the rubber-covered belt, a bump placed at the cutting zone; wherein the first half-part cuts the rubber-covered belt on a tilted portion of said bump. supplying a continuous rubber-covered belt; cutting to size said continuous rubber-covered belt; laying the continuous rubber-covered belt, cut to size, on the forming drum; wherein cutting to size comprises: ▪ carrying a knife formed by a first half-part and by a second half-part above the continuous rubber-covered belt, in proximity to a central portion of a cutting zone; ▪ lifting a lifting element placed below the continuous rubber-covered belt and at the cutting zone, until a portion of rubber-covered belt is lifted; ▪ lowering the single first half-part of the knife, making it slide with respect to the second half-part, until it obtains an opening in said rubber-covered belt and inserting the first half-part in the aforesaid opening; ▪ jointly moving the first half-part and the second half-part along a cutting direction and in a cutting sense for generating a notch in the rubber-covered belt by means of said first half-part; ▪ lowering the second half-part, making it slide with respect to the first half-part until said second half-part is inserted in said notch; ▪ symmetrically moving said first and second half-part (46, 50) synchronously away from each other, in opposite senses and along said cutting direction; ▪ carrying a knife formed by a first half-part and by a second half-part above the continuous rubber-covered belt, in proximity to a central portion of a cutting zone; ▪ lifting a lifting element placed below the continuous rubber-covered belt and at the cutting zone, until a portion of rubber-covered belt is lifted; ▪ lowering the single first half-part of the knife, making it slide with respect to the second half-part, until it obtains an opening in said rubber-covered belt and inserting the first half-part in the aforesaid opening; ▪ jointly moving the first half-part and the second half-part along a cutting direction and in a cutting sense for generating a notch in the rubber-covered belt by means of said first half-part; ▪ lowering the second half-part, making it slide with respect to the first half-part until said second half-part is inserted in said notch; ▪ symmetrically moving said first and second half-part (46, 50) synchronously away from each other, in opposite senses and along said cutting direction; wherein cutting comprises forming, with the rubber-covered belt, a bump placed at the cutting zone; wherein the first half-part cuts the rubber-covered belt on a tilted portion of said bump.