Exactly like CBend stated.
When a team cuts a player, they are no longer responsible for any more bonuses or salary.
However, they are responsible for the "pro-rated" amount of their signing bonuses and any other bonus structures to span more than the year in which it was paid out for.
This is where the "Dead Money" comes into play. It is not necessarily money that we owe to the player, it is money that has been previously paid to the player that must be accounted for towards the Salary cap.