EMB-505 Captain reported they turned to an incorrect heading and flew toward terrain resulting in a CFTT event during arrival. Flight crew corrected heading and continued flight.

Narrative

During the descent to ZZZ; we were instructed to make a turn to a heading and descend to an altitude. While the PM was responding to ATC; I (as the pilot flying) began a turn to the heading. The PM also put in the next altitude. As we began the turn; with the weather being VMC; we realized that one of the mountains we were headed toward seemed too close in altitude to us. Right as we were about to call ATC to ask about our heading; ATC called us and informed us that we were not on the correct heading. This caused a deviation where we had turned to an incorrect heading and went below the maneuvering altitude in that area. We were told a new heading and instructed to climb. We were able to do so and continued from there on a safe approach to ZZZ.The detection of the error was a combination of what we saw outside with the nearby terrain along with ATC inquiring about our heading. Cause: There was a miscommunication along with a failure to verify the new heading we turned to. I believe that the altitude and heading instructions were also using similar numbers; but it has been long enough that I don't remember for sure. We reacted by following ATC instructions and ensuring safe separation from the nearby terrain; both visually and through ATC instructions.Suggestion: Always verify a heading before starting the turn between both pilots. I believe that I began the turn too quickly while other things were occurring. Then it is always important for the PM to actively verify changes once a change has been made.