Today, industrial usage of carbon fiber reinforced plastic (CFRP) is steadily increasing, with an amount of 67 000 ton/yr [“Carbon fibers and carbon fiber reinforced plastics (CFRP)—A global market overview,” Report, Research and Markets Ltd., Dublin, Ireland, 2013]. Products such as the Boeing 787 and Airbus A350 in the aerospace sector, as well as the BMW i3 from the automotive industry consist of more than 50% of CFRP in their structural weight. At the same time, these products also have comparatively high production volumes, e.g., >10 000 cars/yr in the case of the BMW i3 [“BMW undertakes global launch of i3 EV,” see http://www.ihs.com/products/global-insight/industry-economic-report.aspx?id=1065981621, May 20, 2014]. Therefore, a higher degree in automation and cost-efficiency is needed in production. Due to the highly abrasive carbon fibers, conventional machining processes result in short tool life and high costs. Therefore, laser cutting of CFRP as a wear-free alternative has lately become the focus of several research groups. Two different approaches are commonly chosen: cutting by short- and ultra-short pulsed laser systems to reach a process regime of cold ablation and cutting with continuous wave (cw) lasers at high cutting speeds. For the latter approach, it has already been shown that by increasing power and cutting speed, the heat affected zone (HAZ) can be reduced due to less time allowed for heat conduction [Bluemel et al., “Laser machining of CFRP using a high power laser—Investigation on the heat affected zone,” in Proceedings of 15th European Conference on Composite Materials, Venice, Italy (2012)]. Graf and Weber introduced a perpendicular heat flow model, calculating that the required intensity to cut 2 mm of CFRP with a HAZ of 10 μm using a cw laser is 109 W/cm2. The required cutting speed is 8.3 m/s [T. Graf and R. Weber, “Laser applications from production to machining of composite materials,” in Proceedings of EALA, Bad Nauheim, Germany (2012), pp. 289–299]. In this paper, experiments using an ultra-high power fiber laser system of 30 kW to cut CFRP laminates are presented. Although it is not possible to fully achieve the intensities proposed by Graf and Weber, the intensities of approx. 108 W/cm2 of the setup still allow for a practical validation of the CFRP cutting at very high laser power. Due to the high intensities, high cutting speeds per laser pass are necessary. A special experimental setup is chosen with a rotational movement of the specimen, reaching a feed rate of 85 m/s. The heat affected zone was considerably reduced to 78 μm with the 30 kW system, 10% lower than with a 5 kW system under comparable conditions. Although today no scanner systems are available that could handle these high intensities at such high cutting speeds, the experiments still show that processing of CFRP with cw laser systems at highest power has a potential in order to reduce the heat damage to the material.