Are US bills taken out of circulation when redesigned?

No. The US has never withdrawn any bills following a redesign. The only bills that have been officially withdrawn are gold certificates which were recalled when the US went off the gold standard in 1933. All others remain legal tender and can be spent at face value, although that may not make a lot of financial sense if a bill is very old and worth more as a collectible.

Banks are required to hold back old bills that are too worn to continue circulating, and any bills with denominations higher than $100. Thus over time older bills are gradually replaced by new ones, but they're not formally withdrawn due to their design.