Flight crew on approach to SDL Runway 21 reported ATC vectors contributed to flight crew getting GPWS alert.

Narrative

Arriving into SDL; from the north; descending through 7000 ft on the DESRT2 arrival; we were set up to go onto the Guided visual Runway 21. ATC vectored us off the arrival and gave us a heading and told us to descend to 5300 ft. They wanted us to report airfield in sight; but there were clouds; and the layer was scattered; between 7000 and 5300 ft. We got airfield in sight by approx 6000 ft or so; and was given a visual clearance to Runway 21. We were left in a bad position descending and heading towards the rising terrain by the mountains. We were not able to just turn and rejoin the guided visual approach. We had to stop the descent; and turn right; while receiving a caution terrain audible message. We cleared the area; and the message went away. Our descent to the airport resumed and we were now lined up with final Runway 21. We were still approx 2000 feet above the field; while descending to catch up with the VGSI (Visual Glide Slope Indicator) on Runway 21; and we were descending approximately 2000 ft per minute and got a caution descent rate audible. It was instantly resolved with a small correction reducing pitch angle down. We were within stabilized approach criteria prior to 500 ft. agl.Suggestion: Even though we were about 4000 ft. agl when we were given a visual approach; we were left in an uncomfortable position relative to the mountains. It would have been better to just go around and get revectored again.