Short answer. Yes, but only for that matter. Under Article 1926, a general power of attorney is revoked by a special one granted to another agent, as regards the special matter involved in the latter. So the new special power displaces your general agent only for the specific transaction it covers — his general authority continues for everything else.
What the law says
A general power of attorney is revoked by a special one granted to another agent, as regards the special matter involved in the latter.
Civil Code, Article 1926 — General Revoked by Special. Read the full provision →
A special power carves out the general one
Granting a fresh, specific authority to a new agent can cut into the authority of an existing general agent — but only over the particular matter. Article 1926 provides that a general power of attorney is revoked by a special one granted to another agent, as regards the special matter involved in the latter. So if your general agent was empowered to handle your affairs broadly, and you then give someone else a special power of attorney over one specific transaction, the general agent's authority is revoked for that transaction. The special power takes precedence on the matter it covers.
Only for the special matter — the rest survives
The revocation is partial, and the boundary is precise: it operates only as regards the special matter involved in the latter. So the general agent does not lose his whole authority; he loses it only for the specific transaction the new special power covers. For everything else within his general power, he continues to act as before. This means you can hive off one matter to a specialist agent without dismantling the general agency you rely on for the rest. A general agent handling your business generally, and a special agent brought in for a single deal, can coexist — the special power governs the one thing, the general power governs the remainder.
Why the later special grant prevails
The rule follows from what the principal is signalling. By later giving a special power over a defined matter to a new agent, the principal shows that, for that matter, he wants the new agent to act — a more recent and more specific expression of will than the standing general authority. The specific naturally controls the general on the point where they meet, and the later intention prevails over the earlier.
If you appoint a new special agent
If you have a general agent but want a specific matter handled by someone else, appointing that person with a special power of attorney over the matter automatically revokes the general agent's authority on it — you need no separate revocation for that transaction. But be clear that the general agent keeps his authority for everything else, so if you want him out entirely, you must revoke his general power separately. And to avoid confusion or conflicting acts, it is wise to tell the general agent, and any third parties involved, that the specific matter has been reassigned. Clarity about which agent holds which authority is what keeps the two powers from colliding.