Mississippi cut ties with a major Common Core testing provider on Friday, chipping away at the state’s original plans for testing students on the controversial math and English standards.

The state board of education voted to withdraw from the Partnership for Assessment of Readiness for College and Careers, known as PARCC, following months of uncertainty. Last year, a roughly $8 million contract failed to receive approval by the state’s contract-review board, and education officials pushed through an emergency, one-year contract...