Beerwinkel grew up in the Western Cape and attended Porterville High School. In 2009, he was selected to represent his local provincial side, Boland, at the Under-16 Grant Khomo Week competition. He also represented Boland at the premier South African high schoolrugby union competition, the Under-18 Craven Week, in both 2010 and 2011. His performance in the 2011 edition also led to his selection in a South African Schools side, playing one match against France.
After high school, Beerwinkel signed a contract with Pretoria-based side the. He appeared in all fourteen of the s' matches during the 2012 Under-19 Provincial Championship, scoring one try in their 36–37 defeat to the as they finished second on the log. The started both their semi-final win against the same opposition and the final, which they narrowly lost 18–22 against in Durban. At the start of 2013, Beerwinkel made two substitute appearances for a side which won the 2013 Varsity Cup. He was then selected for the South Africa Under-20 that attempted to retain their IRB Junior World Championshiptitle in the 2013 edition held in France. He scored South Africa's first points in the competition, getting a try after just 5 minutes in their first Pool A match against the United States, helping them to a 97–0 victory. He also started their next match, a 31–24 victory over England, and helped South Africa finish the pool stages with a perfect record, playing off the bench in their 26–19 victory against hosts France in their final match of the pool stages. He started their semi-final match against Wales, but couldn't prevent his side slipping to a 17–18 defeat. He was named on the bench for their final match, the third-place play-off against New Zealand, but didn't feature in the 41–34 victory as South Africa secure third spot in the competition. He returned to domestic action, representing the side on seven occasions during the 2013 Under-21 Provincial Championship. In similar fashion to his season with the Under-19s the previous year, his side made it all the way to the final, only to lose to Western Province in the final to finish the competition as runners-up. He once again represented in the Varsity Cup in 2014, this time making seven appearances and scoring a try in their final match against the, but it proved to be a disappointing season for his side as they failed to reach the semi-finals. Three appearances followed for the side during the 2014 Under-21 Provincial Championship and Beerwinkel also scored a try in his side's 123–7 demolition of. Despite Beerwinkel not featuring in the play-offs, the BlueBulls went on to win the trophy, beating 20–10 in the final. Eight appearances followed for UP Tuks in the 2015 Varsity Cup, before Beerwinkel became involved in the ' Vodacom Cup side. He made his senior debut for the Blue Bulls in Round Five of the 2015 Vodacom Cup, coming on as a replacement in their 44–0 victory over Namibian side in Windhoek. A week later, he made his first start for the Blue Bulls in a 40–21 victory over the in Pretoria. He was named on the bench for the ' 2015 Super Rugby season match against trans-Jukskei River rivals the.