When an object moves in a circle with uniform speed, it has a constant change in it’s direction. Since velocity is a vector quantity which has both magnitude and direction, constant change in object’s direction (magnitude (speed) is fixed in this case), makes velocity a varying component. Thus velocity varies at every point in the circular path.
Where as, in case of acceleration, we have only the radial acceleration which always point inward directing towards the center ( the main source to make the object undergo a circular motion by providing required centripetal force). Hence the magnitude and direction is constant, the acceleration is as constant (non zero value) one.
If the acceleration becomes zero, centripetal force ( centripetal force nothing more than a tension that keeps the object in its circular path) required to make the circular motion becomes zero and hence the object no longer go in an circular path