Does putting a +1/+1 counter on a creature with a -1/-1 counter remove both counters immediately?

Whenever a permanent has both +1/+1 counters and -1/-1 counters on it at the same time, state-based actions remove one of each until only one type remains (or both are gone). This is defined in CR rule 704.5q, which states that if a permanent has both +1/+1 and -1/-1 counters on it, each pair is removed as a state-based action.

State-based actions are checked continuously and performed without any player receiving priority (CR 704.1, 704.2). This means the annihilation happens essentially instantaneously — no player can respond to the counters coexisting, because state-based actions are processed before anyone gets a chance to act.

It is important to note this is not a triggered ability or an activated ability — it is a rule the game enforces automatically. The counters simply cease to exist in matched pairs. If a creature has two -1/-1 counters and you add one +1/+1 counter, one of each is removed, leaving one -1/-1 counter remaining.

Concrete example: Your opponent controls a 2/2 creature with two -1/-1 counters on it (making it effectively a 0/0, but kept alive by the counters being separate from its base stats). You cast Battlegrowth to put a +1/+1 counter on it. State-based actions immediately remove one +1/+1 counter and one -1/-1 counter. The creature is left with one -1/-1 counter and no +1/+1 counters.

This rule is especially relevant in formats like original Shadowmoor/Eventide limited, where both counter types appear frequently on the same creatures from different mechanics.