For high school, Boxall attended and played for Mount Albert Grammar School. With Boxall anchoring the defence, Mount Albert won the league title in 2004 and 2005 and placed first at the national tournament in 2005. In his senior season in 2006, Boxall was named the team captain. He led the team to a second Knockout Cup title in three years. They also went to the Auckland Secondary School Soccer Association Championship. Mt. Albert went on to finish second at nationals that year.
Boxall played for a number of teams in his native New Zealand including Ellerslie AFC, Three Kings United, Central United, and Auckland City FC, leading Central United to the 2007 Lotto Sport Italia NRFL Premier title. In addition, Boxall won the NZFC with Auckland City, where he made 6 appearances that year despite scoring zero goals. He was named the Auckland City Young Player of the Year with Central United in 2006 and then again with Auckland City F.C. in 2007.
Boxall was recruited to play college soccer at the University of California, Santa Barbara by head coach Tim Vom Steeg. He followed in the footsteps of other New Zealand players at Santa Barbara such as Tony Lochhead and Neil Jones, both of whom have received senior international caps after appearing for UCSB. In his first season with the Gauchos, Boxall played in 12 games, starting 10 of them. He scored no points and only had one shot on goal, but proved himself to be a solid defensive rock alongside Gaucho defensive stalwart Andy Iro. Boxall's season was cut short due to a knee injury which forced him to miss the rest of the year. Despite missing half the season, Boxall led all rookies with 10 starts and tied for the team high in both yellow cards and red cards, 6 and 1 respectively.
Boxall was selected first overall in the 2011 MLS Supplemental Draft by Vancouver Whitecaps FC. He agreed to terms with the club on 17 March 2011, and made his professional debut on 19 March, in Vancouver's 2011 MLS opener against Toronto FC. After appearing in three matches for the Whitecaps in the 2012 season, Boxall was waived on 22 June 2012.
On 10 July 2012 it was confirmed by the club that Boxall officially joined the Wellington Phoenix of his native New Zealand on a two-year contract. Instrumental in signing Boxall was Ricki Herbert, coach of both the Phoenix and the New Zealand national team at the time. Boxall made his debut for the club on 14 October 2012, in the 1–1 away draw against Melbourne Heart in Round 2. After a beginning to his time in Wellington which saw him play backup to Ben Sigmund and Andrew Durante, Boxall was loaned to the Oakleigh Cannons of the Victorian Premier League. Following a disappointing first season with the Phoenix, Boxall signed a 1-year contract extension on 15 January 2014. Boxall stated the direction that the club was going under new head coach Ernie Merrick was the deciding factor in signing a new deal with the club. In the 2013–14 season, Boxall appeared in 20 games for the Phoenix, starting 18.
Boxall has represented New Zealand at various international levels. His début with the national set up was with the Junior All-Whites (U-20's) in which he made 14 appearances with no goals. During this time, he appeared in the 2007 U-20 World Cup OFC qualifying tournament and ultimately the 2007 FIFA U-20 World Cup. He played in all three U-20 World Cup games before New Zealand were knocked out.
Boxall has also represented the New Zealand U-23 Olympic team, known as the Oly-Whites. He played in all 5 2008 OFC Olympic Qualifiers which saw New Zealand advance to their first ever Olympic Games. At the 2008 Summer Olympics, Boxall again appeared in all three of New Zealand's games before they were eliminated. In addition to these 8 games, he played four Olympic warm-up matches against Central Coast Mariners, Persikota Tangerang, Indonesia (senior squad), and Persija Jakarta between the Qualifying Tournament and the Beijing Olympic Tournament.
Boxall has made 2 appearances for New Zealand A at the Agribank Cup in Vietnam during October 2006, appearing against Thailand and Bahrain. Both games were held at the My Dinh National Stadium in Hanoi, Vietnam.
Only days after making his Whitecaps debut, Boxall was called up to the All Whites' squad for their match against China on 25 March 2011, where he came on as a second-half substitute.
As of 29 July 2015Northern Premier League Champions – 2007
New Zealand Football Championship Champions – 2007
Nedbank Cup: 2016, 2017
OFC Nations Cup: 2016
ACFC Young Player of the Year – 2006 and 2007
All-Big West Honorable Mention – 2008
All-Big West First Team – 2009
NSCAA Third Team All-American – 2010
College Soccer News Third Team All-America-2010
All-Far West Region First Team – 2010
Big West Defender of the Year – 2010