When a bird's beak begins overgrowing it's usually a nutritional problem. In budgies/parakeets, an overgrown or even twisted beak commonly occurs when there's presence of malnutrition as the result of a largely seed only diet. Often there is also liver disease as a result so the overgrown beak is a symptom you shouldn't ignore.
Though eating a mostly seed diet is the top contributor to this condition, it is not always necessary. Sometimes it can happen when they're on a proper pellet and fresh food diet as well.
Some other possibilities are a certain kind of mite, or virus, vitamin/mineral deficiencies (in keeping with nutritional problems usually associated with a seed only diet, or primarily soft food diet, among others). Sometimes it's a serious disease such as PBFD (psittacine beak and feather disease).
Take a look here for more info about your bird's beak and care, plus some options for treatment
No matter what though, clipping it is just addressing the symptom, not the cause. Your little budgie really needs to be seen in order to be diagnosed and then treated.
Find an avian vet near you http://aav.org/vet-lookup and
These days, with birds growing fast in popularity as in home companions, many DVM's are quite experienced and able to see and treat many birds. If you have a pet store that sells birds or know of any bird breeders - ask them who they use for their bird care.
To be sure the vet is a good one, make sure you're there for the exam. This should include hands on, feeling the chest area, peering into the mouth with a well placed flashlight and lifting the tail feathers to examine the vent.
This exam should also include any one or more of the following: Blood tests, gram stains/cultures, x-rays, even oral/crop/tracheal swabs and so on.
If the examining vet doesn't perform a hands on exam, or worse, leaves your bird in their cage or carrier, leave immediately. This is not the vet for you or your bird.
Also note that on weekends, nights and holidays there are vets open. Finding them is often just a matter of calling around and listening to emergency numbers listed on the answering services.
An hour's drive to get help is better than spending an hour at home and not being able to do anything.
Good luck. I sincerely XXXXX XXXXX beautiful feathered friend is ok.