Start by washing your canning jars in hot, soapy water. Keep them warm in a clean sink or dishwasher until ready to use. Place new lids in a small bowl of hot (not boiling) water.
Thoroughly wash sweet potatoes under cool running water. Peel them and cut into uniform 1-inch cubes. Place cut pieces in a bowl of cold water to prevent browning.
In a large pot, bring water to a boil. Add sweet potato cubes and cook until just tender when pierced with a fork, about 10-15 minutes. Don't overcook as they'll continue to soften during processing.
While potatoes are cooking, add 3 quarts of water to your pressure canner and place the rack in the bottom. Begin heating the water.
Using a canning funnel, pack the hot sweet potatoes into hot jars, leaving 1-inch headspace. Don't mash or compress the potatoes.
If desired, add 1 teaspoon of canning salt per quart jar (or ½ teaspoon per pint).
Carefully pour clean, boiling water over the potatoes, maintaining 1-inch headspace. The water should just cover the potatoes.
Remove air bubbles by sliding a plastic spatula or bubble remover tool between the potatoes and jar. Add more water if needed after removing bubbles.
Clean jar rims thoroughly with a damp paper towel. Center lids on jars and apply bands until fingertip-tight – don't overtighten.
Place jars in pressure canner. Lock lid and bring to a boil over high heat. Let steam vent for 10 minutes, then add weight or close petcock. Process pints for 65 minutes or quarts for 90 minutes at 11 pounds pressure (adjust for altitude).
When processing is complete, turn off heat and let canner depressurize naturally. Don't force cool the canner.
Once pressure gauge reads zero, wait 5 minutes, then carefully remove canner lid. Let jars sit in canner for 10 minutes before removing.
Remove jars and place on a towel-lined counter away from drafts. Let cool undisturbed for 12-24 hours.
Check seals, remove bands, label jars with date, and store in a cool, dark place.