Timmins was born in Dunedin.[1] His father, Brendon Timmins, played rugby in Otago during the 1990s and in Southland in the early 2000s.[2] While living in Southland, Sam played rugby for Eastern Hawks and Star.[2]
When he was 11 years old, his family moved to Japan after his father became a rugby coach for the Mitsubishi Sagamihara DynaBoars.[3] Back in Dunedin, he was heavily involved in rugby until age 12, playing as a lock and Number 8 for the Kaikorai club. He grew up playing social basketball, but only began to take the game seriously after arriving at Otago Boys' High School.[4]
In 2013, Timmins joined the Otago Nuggets and made his New Zealand National Basketball League (NZNBL) debut. At age 15, he became the youngest debutant in Nuggets history.[5] A stress fracture in his back sidelined him for the entire 2014 season.[6] That year, he led Otago Boys' High School to the National Schools Championship and was named tournament MVP.[6] He also helped the Junior Tall Blacks come within three points of winning the Under-18 Oceania Championship final.[7]
In January 2015, following the collapse of the Otago Nuggets, Timmins moved to Christchurch to play for the Canterbury Rams and attend Middleton Grange School.[7] In his debut for the Rams, he had 20 points and nine rebounds.[8] In 16 games during the 2015 season, he averaged 5.7 points and 3.4 rebounds per game.[9]
As a freshman in 2016–17, Timmins saw action in 31 games including 18 starts and averaged 3.2 points and 3.8 rebounds while adding 20 blocks and shooting 48.9 per cent from the field. He had a season-high 12 rebounds on two occasions, with his season high in points being 11.[13]
As a sophomore in 2017–18, Timmins started in all 34 games and averaged 4.3 points and 4.6 rebounds per game. He set a career high during the season with 13 points against Kennesaw State.[14]
As a junior in 2018–19, Timmins competed in all 36 games while shooting 62 per cent from the field (31-of-50) and averaging 1.9 points and 2.2 rebounds per game. His minutes dropped from 18.0 per game as a sophomore to 10.4 per game as a junior.[15] He had a season-high nine points against UCLA, and had a season-best seven rebounds against Utah while also recording a career-high-tying four blocks.[14]
As a senior in 2019–20, Timmins averaged a career-low 7.9 minutes per game to go with 2.0 points and 1.4 rebounds in 31 games.[15]
On 30 June 2021, Timmins signed with the New Zealand Breakers of the Australian National Basketball League (NBL) on a one-year development contract, with a club option for a second year.[25][26] On 15 April 2022, he was elevated to the full roster following the departure of Yanni Wetzell.[27] In 15 games during the 2021–22 NBL season, he averaged 3.3 points and 2.3 rebounds per game.[28]
On 12 July 2017, Timmins was invited to a six-day Tall Blacks camp in Auckland, ahead of a final 12-man roster being named to travel to the FIBA Asia Cup in Lebanon, via preparation matches in China.[39]
In July 2023, Timmins was named in the Tall Blacks squad for the 2023 FIBA World Cup.[40] He re-joined the Tall Blacks for qualifiers in February 2024.[41]
Timmins is the son of Brendon and Karen Timmins, and has a sister named Ruby.[2][7] His father played 74 games for the Otago rugby team and 42 games for the Highlanders, while his mother played netball for Southland. His grandmother, Sandra McGookin, was a six-time New Zealand javelin champion.[42]