If your deck will be built above a concrete patio it is always best to have the deck footings in place before the patio is installed. However, if the patio exists you will need to cut openings in the patio in order to install your frost footings. Using a sledge hammer or jack hammer can break up the patio but will leave a broken edge and will likely crack the entire slab.
If you want a small, clean hole this must be done by using a diamond bladed concrete saw. These tools are expensive and require some skill. You may want to consider hiring someone to do this for you. If you decide you are up to doing it yourself remember to pay special attention to safety. Cutting concrete will be extremely noisy, and dusty. You should wear ear and eye protection and be careful not to breathe in the concrete dust. Once the footings are in place you may be able to refinish the surface of the patio to its original condition.