Bursey had a two-round total of 146 after an opening-round 71.
The 20-year-old from Gander is entering his junior year at Utah Valley University on a golf scholarship.
Bursey had a tough day Tuesday with six bogeys and one double. He birdied three holes.
None of the other four Newfoundlanders made the cut at the Amateur. Jaron Flynn of St. John’s had a two-day total of 153 (73-80), Nikashantess Penashue of Sheshatshui carded a 154 (75-79) and Mike Furlong of St. John’s, the defending provincial champ, had a 165 (83-82). Grant Lane of St. John’s also missed the cut.