The Bison played just two games under Mraz before the 2020 campaign was cancelled.

A veteran of more than 30 years of coaching at both the collegiate and international levels, currently and will continue to serve as the head coach of the Czech Republic Womens National Team. He guided them to a fourth-place finish at the 2019 European Cup and saw four players finish in the top 10 in scoring. The team set European Cup records for most goals scored and fewest goals allowed, and were invited by the Federation of International Lacrosse (FIL) to compete at the 2021 World Games in Birmingham, Alabama. They will also compete for the World Cup in 2021.

Mraz who served two stints as the head coach of the Fairfield University womens club lacrosse program (2012-16; 2018-19) spent the 2017-18 school year as an assistant coach at William & Mary, which is a member of the Colonial Athletic Conference (CAA). He worked directly with the Tribe goalkeepers and was instrumental in the development of both offensive and defensive game strategies while assisting with recruiting and practice planning. Mraz saw two student-athletes earn CCC Rookie of the Week honors while another earned Defensive Player of the Week accolades, and a fourth received All-Rookie Team honors.

As the head coach of Maine Maritime in 2016-17, Mraz helped the Mariners establishes a single-season program record for wins as they advanced to the semifinals of the North Atlantic Conference (NAC) for the first time in school history. Maine Maritime set a total of 34 school records during his time as head coach, and the team earned International Womens Lacrosse Coaching Association (IWLCA)/Zag Sports Academic Honors.

Mraz began his collegiate coaching career in 1993 as an assistant with the startup mens lacrosse program at Fairfield University. In four seasons with the Stags, Mraz helped the program record their first winning record in 1996 and advance to the Metro Atlantic Athletic Conference (MAAC) playoffs. He then returned to the collegiate ranks albeit on the womens side in 2014 when he joined the University of Bridgeport. He spent two seasons with the Purple Knights, helping them win a program-record 12 games in 2015 while establishing school records for both goals/game (12.94) and goals against average (GAA) (7.53).

Mraz co-founded the Wakemans; Boys and Girls Lacrosse Club in 1988 and worked as head coach of their Girls Elite Travel Teams until 2016.