An outdoor drain is not different from any other drain in that they are all made to take wastewater and deposit it into a main sewer line or a septic line. The crucial difference between a household drain and an outdoor drain are the substances that will can block a pipe. Organic intrusions of tree roots are possible, as are all of the waste deposits from households like soap scum from washers, lint, sand, dirt and debris, grass clippings and even small rocks and pebbles. To fully clean an outdoor drain, you will need a specialised power tool.
Rent a power auger from your local hardware store. A power auger is essentially a motorised, heavy-duty, self-propelled snake.
Pry off the cover of the outdoor drain or remove the mounting screws, if applicable.
Plug in the power auger and begin to feed the auger down into the drain. Turn the auger "on" as you feed it down the drain line and make sure the rotation is in a clockwise direction. A switch on the auger controls this feature.
Feed the auger down the drain as it rotates. The rotating motion often slows or bogs down at the actual clog in the drain. Reverse the rotation to counterclockwise, pull back on the auger a few feet and then switch it back to a clockwise rotation and feed it back in. Continue this cycle of backward and forward movement until the clogged area clears.
Using a plumbing clean-out tape to break through the clog is a temporary solution at best. A power auger will literally grind away any obstruction in the drain and virtually remove it, while a clean-out tape will merely punch a hole in the clog. The hole will quickly fill in again after a few drain cycles, and you will need to address that same clogging situation once again.