We demonstrated the measurements of attenuation constant of a multi-mode fiber with 300-micron core diameter and 1-km length at 1070 nm. The observed attenuation constant was below 0.7 dB/km, the laser power of 5 kW was coupled into the 1-km fiber at 1070 nm, and the overall transmittance was 85%, and the first Raman Stokes signal was observed in the transmitted laser spectrum. We demonstrated concrete cutting with a 4-kW fiber laser at 1070 nm. The slab thickness was 100 mm. This technique can be extended to thick concrete slabs more than 1 m without increasing laser power.