The project isn’t going to destroy large pieces of debris with lasers — that would just break targets up into smaller and more dangerous pieces of space junk. China found this out first hand in 2007 when they tried to destroy one of their own defunct satellites — it broke up into small pieces, creating a dangerous debris field.
Instead, the plan is to make a laser that is capable of tracking and targeting smaller pieces of debris less than 4 inches across and zapping them. This would ideally have one of two outcomes — either the debris will be pushed out of the way to prevent a collision or it will cause the small pieces of debris to burn up in the atmosphere.
The idea might not make it off the ground though. Many fear that this space debris laser could potentially be used as a weapon against targets on Earth. If that is the case, it could mean that the laser violates the Outer Space Treaty of 1966 that was put in place to ensure that space could not be weaponized.