The single mode fiber laser cutting of two types of continuous fiber-reinforced thermoplastic composites (TPC) with polyamide 6 (PA6) matrix and a fiber content of 60 wt\% was investigated: a glass fiber-reinforced composite (PA6/GF60) and a carbon fiber-reinforced composite (PA6/CF60). Preliminary, the thermal properties of the composites were analyzed to derive the cutting mechanisms. Thermogravimetric Analysis (TGA) showed decomposition onset temperatures of 457.6°C for the PA6 matrix and 737.3°C for the carbon fibers, while no thermal decomposition of the glass fibers was detected up to 1,000°C. In consequence, the single mode fiber laser cutting of the PA6/GF60 composites required a significantly higher number of cutting cycles in conjunction with an increased heat affected zone (HAZ) as compared to the PA6/CF60 composites. Analysis of the HAZ and the mechanical properties of the laser cut composites by optical microscopy and uniaxial tensile testing showed an anisotropy and dependency on the laminate structure. However, the obtained mechanical properties of the laser cut composites were found comparable to their water jet cut counterparts.