Dishwashers can be either hardwired, or cord-and-plug connected. Check the owners manual of the unit you have, but in most cases the decision is left to the installer.
From a random Maytag Dishwasher Installation Guide (PDF)
In newer homes you'll commonly find a 125V NEMA 5-15R receptacle supplied by a 20 ampere circuit, used to supply a dishwasher and disposer. In this case, the receptacle is typically installed in the cabinet under the sink. If you don't have a receptacle under the sink, it's not likely that the dishwasher is cord-and-plug attached.
The National Electrical Code, specifies that all outlets must be accessible. Because of this, a receptacle installed in a location that requires the removal of the dishwasher is not code compliant. i.e. If you can't find where the dishwasher is plugged in, it's likely hardwired.
Checking the wiring for the disposal, might give you some clues as to how things are wired.
You might also find This answer useful, when trying to figure out what you can connect to the circuit.
Code that allows Garburators and dishwashers to be cord-and-plug-connected
National Electrical Code 2014
Article 422 Appliances
II. Installation
422.16 Flexible Cords.
(B) Specific Appliances.
(1) Electrically Operated Kitchen Waste Disposers. Electrically operated kitchen waste disposers shall be permitted to be cord-and-plug-connected with a flexible cord identified as suitable for the purpose in the installation instructions of the appliance manufacturer, where all of the following conditions are met:
(1) The flexible cord shall be terminated with a groundingtype attachment plug.
(2) The length of the cord shall not be less than 450 mm (18 in.) and not over 900 mm (36 in.).
(3) Receptacles shall be located to avoid physical damage to the flexible cord.
(4) The receptacle shall be accessible.
(2) Built-in Dishwashers and Trash Compactors. Built-in dishwashers and trash compactors shall be permitted to be cord-and-plug-connected with a flexible cord identified as suitable for the purpose in the installation instructions of the appliance manufacturer where all of the following conditions are met:
(1) The flexible cord shall be terminated with a grounding type attachment plug.
(2) The length of the cord shall be 0.9 m to 1.2 m (3 ft to 4 ft) measured from the face of the attachment plug to the plane of the rear of the appliance.
(3) Receptacles shall be located to avoid physical damage to the flexible cord.
(4) The receptacle shall be located in the space occupied by the appliance or adjacent thereto.
(5) The receptacle shall be accessible.
Here are a couple of ideas. Usually there is a service panel on the outside of the house, this is where the main service line connects to the home. There should be a few breakers in there, but they are typically only for the bigger circuits. At my house for example, there are breakers in the outside panel for the range/oven, dryer, air conditioner, and one that goes to my main circuit panel inside. The inside breaker box is where all the breakers for lights and outlets inside are. Some homes get a second panel added inside when they run out of space on the primary panel. So I'd try to see if you have another circuit panel inside, or check in your outside panel to see if there is a circuit there that will shutoff the dishwasher circuit.
Best Answer
For a hardwired appliance, either one of two things are true in order for the connection to comply with Code:
If it's the former, then the drywall damage is pure sloppiness (and wouldn't qualify as "neat and workmanlike" if you ask me -- some sort of LV bracket could be used for cable routing purposes I suppose?). If your dishwasher does the latter (which is my suspicion), then you need to install a box and NM clamp for the cable (a surface mounted "handy box" would do, as would an old work box cut into the wall) and then use a faceplate with a knockout on the front along with a cable clamp or bushing to route the appliance whip into the box.