Can you activate a planeswalker's minus ability if it would bring its loyalty below zero?

Loyalty abilities have loyalty costs that either add or remove loyalty counters. A loyalty ability with a negative cost (e.g., −3) requires you to remove that many loyalty counters as the cost of activation. You can only activate such an ability if the planeswalker has enough loyalty counters to pay the cost — meaning it must have at least that many counters on it before activation.

Under CR 606.3, a loyalty ability's cost is paid by adding or removing loyalty counters. Crucially, CR 606.3 states you cannot activate a loyalty ability with a negative loyalty cost unless the planeswalker has at least that many loyalty counters on it. In other words, the loyalty cannot go below 0 as a result of paying the cost — you need enough counters to cover the minus cost exactly or have more remaining.

Note that it is legal to activate a minus ability that brings the planeswalker to exactly 0 loyalty. The planeswalker will then be put into the graveyard as a state-based action (CR 704.5i) after the cost is paid, but the ability still goes on the stack and resolves normally.

Example: You control Chandra, Torch of Defiance with 2 loyalty counters. Her −3 ability cannot be activated because you only have 2 counters and the cost requires removing 3. However, her −7 ultimate similarly cannot be activated unless she has at least 7 counters. If she had exactly 3 counters, you could activate the −3 ability, she would drop to 0, be put into the graveyard by state-based actions, and the ability would still resolve.