From a technological perspective it is difficult to do.
The Gulf Stream carries 1.4 × 10^15J/sec heat flux (from the Atomic Rockets "Boom Table" http://www.projectrho.com/public_html/rocket/usefultables.php), while human civilization has an energy output of 1.5 × 10^13J/second in the year 2004.
So human civilization is outmatched by two orders of magnitude in terms of energy output by the Gulf Stream alone.
The second consideration is the Gulf Stream is powered by the rotation of the Earth and the heat energy delivered to the oceans by the Sun (both directly and indirectly through the atmospheric heat engine, the winds). The magnitude of these energies is even greater:
1.7 × 10^17J total energy from the Sun that strikes the face of the Earth each second
2.1 × 10^29J Earth's rotational energy (no time factor given)
While you could imagine some sort of gigantic dam or massive turbines trying to counter the flow of the Gulf Stream, you wold be essentially be pushing against a massive wall of moving water which would attempt to flow to areas of lower energy potential. You can imagine the consequences of that much energy and that mass of water being "bottled up", when the "dam" bursts the consequences will be catastrophic.
Of course technology isn't 100% efficient anyway, even the most optimistic plans to harvest the energy of the Gulf Stream using underwater turbines only suggests a range of 3-10 GW of energy can be extracted; only 1/3 of Florida's annual energy consumption.