Born in Onaga, Kansas, Griffis moved with his family to Rat Portage, Ontario, where he excelled in many sports, including ice hockey.

[3][a] Renamed the Kenora Thistles in 1907 — the city had changed its name in 1905 — the team remained a powerhouse, and Griffis (along with fellow future Hall of Famers Art Ross and Tommy Smith) was a key member of the Thistles' January 1907 Stanley Cup winning team when they defeated the Montreal Wanderers in a two-game total goal series, the only games in the entire season which the Wanderers lost.

Signed in 1919 on an emergency basis at age 35, he played only two games for Vancouver in 1919, as well as in its playoff loss that season to the Seattle Metropolitans.

[12] Si Griffis, standing at 6 feet and one inch, was one of the tallest players of his era but he was nonetheless also one of its fastest skaters.

During the 1912–13 PCHA season – on January 15, 1913 – league executive Frank Patrick organized a speed skating contest between four players considered to be the fastest in the Pacific Coast Hockey Association: Si Griffis, Ken Mallen, Fred "Cyclone" Taylor and Ernie "Moose" Johnson.

Before the contest Griffis was confident regarding his chances of winning it all, due to his quick first steps, but in the final heat he was nonetheless beaten by Ken Mallen of the New Westminster Royals by a slim margin.