Revise your deck plans to allow for the needed opening. Consult with an engineer or architect, especially if the opening interrupts more than one or two joists, as well as your building inspector or permits department. Add additional beams or posts if recommended by the engineer, architect or jurisdictional officials to meet building codes to support a deck with a large opening.
Double the joists on both sides of the opening. For example, hang two rather than one 2-by-8 joists from double joist hangers running between the ledger attached to your house and the rim joist farthest from the house. Cut a double header out of the same size lumber, typically 2-by-8 for joists, although it can sometimes be larger or smaller, to run between the double joists on each of the remaining two sides of the opening. Hang these double headers from double joist hangers as well. Connect all joist hangers to joists and headers with galvanized joist nails.
Cut single joists to connect the doubled headers to the ledger and rim joist. Nail them in place with galvanized joist nails to hold the single joist hangers.