There are two kinds of lasers, continuous wave (CW) and pulse. Since you're thinking of CW, that is what I will address.
Most CW lasers work by reflecting light back and forth between two mirrors. A certain amount of energy is pumped into that system and that results in a monochromatic beam that (within some degree of precision) is in-phase with itself. One of the two mirrors will be only partially silvered (or in certain cases, missing) and so a portion of the laser beam crosses to the exterior and is available for use.
If both mirrors are 100% reflective, then you might think that the more energy you pump in, the more that would accumulate in the laser in the form of a steadily power-increasing laser beam. To some extent, this is true. But what will happen is that the elements responsible for pumping energy into the beam (the ionized gas, crystal, or semiconductor) will reach a limit where they are absorbing as much energy as they are pumping into the laser beam.
At that point, the laser beam will remain at that power limit (or possibly begin reducing) as the equipment uses the remaining energy to produce heat.