Christ routinely used hyperboly to make His point. He simply meant to not hold on to anything that is causing you to not live the full Christian life.
Whether it be your job or home or relationships, if it’s causing you to compromise your Christian experience, get rid of it.
In the Catholic Act of Contrition, we say, “I firmly resolve, with the help of thy grace, to sin no more, AND TO AVOID THE NEAR OCCASION OF SIN.” Sounds like the same thing.