Concrete cutting at construction sites causes problems such as noise, vibration, and dust. In particular, during the demolition and renovation work on buildings in urban areas, protection against noise, vibration, dust, etc., is needed. Concrete cutting using a CO2 laser was investigated 20 years ago. However, this method had never used because the equipment is difficult to carry. In this study, we used a portable fibre laser, which is convenient to carry. Two types of concretes with different strengths were prepared for the experiment. High-strength concrete has never been used in similar research before. High-strength concrete is just only used for skyscrapers because of its high quality and costs. Furthermore, it has already been used for skyscrapers in Japan. It is for this reason that we chose to use it in this study. Irradiation measurements were conducted under various conditions using laser powers of 6 and 9 kW. It was confirmed that the cutting effectiveness of CO2 and fibre lasers was approximately identical for concretes with a thickness of 200 mm. Furthermore, the cutting effectiveness for the two concretes with different densities was almost the same. However, the situation after cutting was different because the vitrification of the cutting and glass formation progressed in low-density concrete and an explosion phenomenon occurred in high-density concrete, simultaneously. This study suggests that laser concrete cutting can be used as a solution when noise and dust are major problems.