Wooden decking is subject to deterioration from weather and pests, whatever the wood used in its construction and however it is finished. This is especially true for joists, because they stay wet longer after rainfall and water tends to collect between them and the decking boards. They also provide a shady home for wood-boring insects and other pests. You can replace the rotting joists one by one after you remove the decking. If the rot is extensive, you may want to consider replacing them with pressure-treated wood.
Decking board removal
Remove one board at a time. If the boards are screwed in, use a drill to remove the screws and lift off each board in turn.
Pry up boards that are nailed down by first hooking the crow bar under the board and prying it up about 1.25 cm (1/2 inch), then hooking the bar around the nail head and pulling the nail out. Use a piece of wood to lever the bar so you don't damage the decking.
Remove as many boards as is necessary to completely uncover the rotted joists. If the joists are hung from beams on the front and back of the deck, you will have to remove all the decking.
Remove all nails from the boards and put them aside.
Remove any nails or screws holding the joist to posts or beams. If it is secured to beams by joist ties, remove the nails holding the joist and lift it out, leaving the ties in place.
Measure the length of the joist you have removed and cut a new one to the same length with a circular saw. Drop it into place so that it is held by the joist ties and reattach it to the beams or posts with 7.5 cm (3 inch) screws or nails.
Use joist nails or 3 cm (1 1/4 inch) screws to secure the joist to the ties.
Repeat this process for any other rotten joists.
Replace the decking. If you are using nails, change their position since they won't hold the boards for long if pounded into their original holes. Screws are preferable to nails for securing decking, so it's probably a good idea to replace the nails that you remove with 7.5 cm (3 inch) deck screws.
Work from below, using a ladder if necessary, if you can't access the joists safely from above.
Wear protective goggles when cutting with saws or using a hammer.
Never put your hand in front of a moving saw blade.