Scott Woodard started his career at Western New Mexico University, first as a student, where he received his Bachelor's degree in Biology while playing baseball. He was part of the team that won the first Rocky Mountain Athletic Conference Championship and was twice named First Team All-Conference as a shortstop. After his bachelor's, he moved on to earn his Master of Arts in School Administration, also from WNMU, while being the assistant coach to the program. Woodard, in this tenure, leads the team to national recognition, securing 3rd in the standings and coming one game shy of advancing to the NAIA World Series.

Woodard took a short break afterwards from WNMU and went to coach at Tularosa and Deming High Schools in New Mexico. Woodard came back to Silver City in 1992 to take over as head coach for the baseball team. In 1993, he eventually joined as Assistant Athletics Director to the legendary Dick Dragmiester, who eventually handed the position of Athletics Director to Woodard, following his retirement.

During the 15 years he served as Athletics Director, Woodard facilitated various athletics improvements, including building the softball field and making renovations to the basketball facility. He was also the main overseer of the building of the Altamirano Football Stadium and the Fox Complex, which houses the locker rooms, weight room, and also facilitated the building of three tennis courts, which enabled Western to host home tennis contests. Scott Park Golf Course, also under his supervision, saw a new driving range, chipping and putting area, coach's facility, and restrooms added to the course.
Woodard spent more than half his life at the university as a student, athlete, coach, and administrator. He has held nearly every job in the department, including sports information, game management, compliance, and eligibility.

After his illustrious tenure at WNMU, Woodard moved over to Arizona State, where he was an assistant coach and recruiting coordinator from 2011 – 2013. His guidance helped the Sun Devils in their back-to-back WCWS appearances, accumulating over 50 wins each season. Woodard then moved to the Southeastern Conference, where he served for 5 years (2013 – 2017) as assistant coach for Auburn University, where he accumulated 40-plus wins seasons back-to-back Women's College World Series appearances, which included making the WCWS Finals in 2016. Woodard also helped develop 13 All-SEC performers while at Auburn University.

Woodard then moved to the University of Alabama – Birmingham (UAB) as staff and assistant coach, working primarily with hitting and recruiting duties.
Woodard is currently the fielding coach for the Texas State University Bobcats. He has been part of the Sun Belt Tournament in 2024 and 2025 regular-season titles. He is also one of the 2024 NCAA Division I South Region Coaching Staff of the Year award winners when the Bobcats won the Sun Belt title and their second consecutive NCAA tournament berth.
As of 2026, Woodard will enter his fifth season on the Texas State coaching staff, heading to the 2026 season with his role being the Bobcats' fielding coach.

Woodard was inducted into the WNMU Hall of Fame in September 2017.