In December 2002, Aksalu was included in Flora's first team squad for pre-season training. During his first seasons with the club, he mostly played for the club's reserve side Tervis Pärnu. Aksalu became a regular starter for Flora in the 2006 season. His first trophy with Flora came in the 2007–08 Estonian Cup.
On 29 January 2010, following a successful trial, Aksalu signed a two-and-a-half-year contract with Championship club Sheffield United for a transfer fee of £180,000. Kevin Blackwell, Sheffield United's manager at the time, claimed Aksalu was the best goalkeeping triallist he had seen in a long time and had the potential to become Estonia's number one. However, Aksalu failed to impress new manager Gary Speed and was unable to break into the first team. On 6 October 2010, Aksalu joined Conference National club Mansfield Town on a two-month loan. He remained sidelined through most of his spell due to an abdominal muscle problem, making only three appearances before returning to Bramall Lane in December. After a lengthy spell on the sidelines following back surgery, Aksalu was released by the club on 19 January 2012.
Return to Flora
Following his release, Aksalu returned to Estonia and began training with his former club Flora to regain his fitness. He rejoined the team on 9 April 2012.
SJK
On 4 April2013, Aksalu signed a one-year contract with Ykkönen club SJK. He made his debut for the team on 4 May 2013, in a 2–1 home win over PK-35 Vantaa. SJK won the 2013 Ykkönen and were promoted to the Veikkausliiga. In October 2013, Aksalu signed a new two-year contract with the club. On 24 August2015, his contract was extended to 2017. Aksalu won the Veikkausliiga title in the 2015 season. He was named league's Best Goalkeeper and SJK's Player of the Year. Aksalu was named club captain ahead of the 2016 season. On 24 September2016, Aksalu helped his team win the 2016 Finnish Cup by saving two penalties in a shootout against HJK in the final.
International career
Aksalu has represented Estonia at under-16, under-17, under-20 and under-21 levels, amassing 20 youth appearances overall. He made his senior international debut for Estonia on 17 October2007, playing the first half of a friendly match against Montenegro, where he conceded the only goal of the game. In 2015, he succeeded Sergei Pareiko as Estonia's number one goalkeeper.