Question

how does powerful laser's cut object

Answer 1

The laser beam simply melts the material hence cutting through it.

Answer 2

Lasers are generally made by using alpha rays beta rays and most powerful gamma rays.
alpha rays can pass through metallic foils
beta rays can pass through the block of the wood.
and gamma rays and its nearly Xrays can pass through any object accept metals.
It can pass through our bones also.

The most powerful laser technology is not now used but planning for that.
Gamma rays are formed by Group of or bundles of neutron particles with max. velocities.
And neutron is made up of an electron and a proton. which cancel out each others energy.
so gamma rays can be used in powerful lasers

due to the cancelled energies it does not attract over any anodes or cathodes.

This neutrons are given out by radioactive elements.

Due to no attraction it goes out or thrown out from nucleus with about more than 10 thousand m/s velocity and travels the straigh without hitting any thing.
Thus , it has tendency to cut any object.
due to its high speed.
(speed of electrons revolve around the atom is nearest to the speed of light)