In addition to the mounting clips holding the cooler onto the board, the heatsink itself is typically affix to the chipset using a thermal compound such as thermal tape. Trying to pull the heatsink off at this point could damage the board and chip. This thermal compound needs to be removed.
Take a hairdryer and set it to a low heat setting. Gently aim the hairdryer towards the back of the board to slowly raise the temperature of the chipset. This heat will eventually loosen then thermal compound used to affix the heatsink to the chipset.
