Why doesn't the magnetic force change the velocity of a particle?

Well actually, it does. Remember that the velocity is a vector and so is the force. Since F=ma, the acceleration due to a given force points in the same direction as the force itself. The magnetic force is perpendicular to the direction of motion, and hence so will the acceleration. And we know that when the acceleration is perpendicular to the velocity of a particle, it undergoes uniform circular motion. So, the magnitude of the velocity remains unchanged when the particle is acted upon solely by a magnetic force. Yet, as we just said, the velocity is a vector and hence it is defined by both is magnitude and direction. Since the direction changes, the velocity vector also does change. We call such an acceleration (which is always perpendicular to the velocity) normal or centripetal, as it makes the particle circle around a certain point.