You dont define what it means to cut easier, but I will address how you select wavelength to cut faster and how you can select wavelength to be more precise in your cuts (although this precision likely does not matter for the vast majority of laser cutting applications)
For lasers that differ only in wavelength, you would typically want to select the wavelength with the highest absorption in the material you want to cut, if everything else was equal. Photons that are reflected or transmitted through the material won't transfer their energy to the matetial you are cutting and therefore wont contribute to the cut. This way you maximize cutting speed. Obviously other considerations come into play with practical lasers, with laser power being a big one.
If you want to do extremely high precision cutting (micro/nanoscale), you will tend to want a shorter wavelength. Lasers with a shorter wavelength can be focused to a smaller spot size, increasing precision. This is only important at micro or nanoscale cutting.
There are other ways a laser can cut a material than by direct absorption in the material to cut, but I will ignore those for this answer since you have control of the laser wavelength.