To waive a player is to release them from their contract. The team keeps paying any guaranteed salary as dead money, and the player becomes a free agent. "Waive and stretch" means releasing them and spreading the remaining money over extra seasons.
In HoopSim you cut a player from the Roster tab; there is no claim period, and the player goes straight into the free-agent pool. Guardrails apply: a roster floor of 8 players during the season, training camp and preseason (none in the offseason), a limit on cuts per hour, a ceiling on one season's dead money, and commissioner approval to cut a star. Cutting a player ends your Bird rights on them and returns any equipped ability card to your bench. A trade that would push a team past its roster limit carries that team's cuts with it. See also the stretch provision for spreading the hit.
Rulebook: Dead money. Related: dead money, stretch provision, buyout.