Yes, an object can be moving at the same time that it is also slowing down. During this period, its acceleration is in the opposite direction of its velocity.
One example of an object having a northward velocity and a southward acceleration is a ball thrown upward. The velocity of the object will depend on the strength of the throw, while its acceleration would be -9.8 m/s/s, since it is going against gravity. As this negative acceleration overcomes the ball's velocity, it will reach its maximum distance and fall back toward the ground. This time, during the free fall, the velocity and the acceleration are already in the same direction.