Laser cutting of paper is widely used in the paper conversion industry. CO2 lasers are well suited for this type of applications. Desktop printing is a large market both for digital photography, document management and graphics applications, but it still lacks advanced cutting and scoring ability, and CO2 lasers seem costly to be integrated in mass-market printers. For that reason, mass-scalable and low-cost semiconductor laser diodes would be very advantageous to add paper cutting and scoring features in desktop printers. However, common paper can not be cut properly using visible or Near Infrared (NIR) laser diode since it has a very poor absorption at these wavelengths. We report here an innovative solution to achieve paper cutting or scoring using a 1 W single emitter NIR laser diode, within an inkjet printer. A special ink that absorbs the NIR light, and that penetrates all through the paper, is first disposed on the lines to be cut. Then, the laser diode goes along the lines to be cut. We show that a cutting speed of 2m/min can be achieved on 80g/m2 conventional paper. The influence of the optical properties of the ink on the cutting speed are discussed, as well as focussing issues. In particular, we show that invisible inks are suitable, and very clear-cut edges can be obtained. The perspective of this technique are discussed.