How do rockets spin and pitch at the same time? Thrust vectoring using a gimbal which basically just always faces down, so that shouldn't cause it to pitch. Since the rocket is spinning, using the fins to pitch wouldn't work unless they only activated for a portion of each rotation. Using the fins in such a manner seems like it would be extremely difficult and prone to malfunction.
EDIT: I'm specifically talking about the rockets we use today. They launch upright, and generally arc before they release their payload, while spinning along their vertical axis. The Saturn V is one example of this.
Best Answer
There are multiple methods of control, and they depend on whether the craft is still in the atmosphere or in vacuum, and if you only have a single engine on centerline, or if you have multiple engines.
Any method that provides side thrust can provide roll control as long as it is not on the centerline. Multiple engines, side thrusters, and movable fins can all work.
In the case of the shuttle, the main engines were away from the centerline and had plenty of authority to roll the craft in flight by gimballing. The Saturn V first stage had four outboard engines that could gimbal to control roll, pitch, and yaw. The Saturn I (which had only one main engine on centerline) had an auxiliary propulsion system (APS), which were smaller thrusters. These provided roll control in flight (among other functions).