No, for Taoists there is no formal day off like Saturday or Sunday.
As you know, the need to act may not fit a convenient, “do nothing on this day” principle. You may have to do stuff on Saturday and Sunday. The need to engage in rest, to have communal time, and also to spend time in isolation is well understood as part of the art of living well. Part of creating a happy and sustainable life for oneself is setting aside enough personal time for self-care. Doing that may require much more than a single day. Coming to understand the art of living will help one to determine how much time to commit.
In some lives, it is also understood that the first part of one’s life is committed to work, family, and society. The later portion of one’s life can then be fully committed to spiritual pursuit when one renounces the human world. This is the Sabbath of one’s life.