Coredata delete all data in an entity
let appDel: AppDelegate = UIApplication.sharedApplication().delegate as! AppDelegate
let context: NSManagedObjectContext = appDel.managedObjectContext!



The type annotations are not necessary, the Swift compiler can infer
the type automatically:

let appDel = UIApplication.sharedApplication().delegate as! AppDelegate
let context = appDel.managedObjectContext!





request.returnsObjectsAsFaults = false



This makes no sense here because you don't want to access
any properties of the returned objects. On the contrary, only the
managed object ID is needed to delete objects and no properties need
to be fetched at all, so this should be replaced by

request.includesPropertyValues = false


to increase the performance.



I prefer to cast the return value from the fetch request immediately

let incidents = try context.executeFetchRequest(request) as! [NSManagedObject]


this makes both the type annotation : AnyObject and the cast
as! NSManagedObject obsolete.



You have to decide how an error should be handled, but I would
at least print some message when running in debug mode

} catch let error as NSError {
    debugPrint(error)
}


to detect possible problems.



Starting with iOS 9, objects can be deleted directly in the store
without loading them into memory.
This would look like this:

func deleteIncidents() {
    let appDel = UIApplication.sharedApplication().delegate as! AppDelegate
    let context = appDel.managedObjectContext!
    let coord = appDel.persistentStoreCoordinator

    let fetchRequest = NSFetchRequest(entityName: "Incidents")
    let deleteRequest = NSBatchDeleteRequest(fetchRequest: fetchRequest)

    do {
        try coord.executeRequest(deleteRequest, withContext: context)
    } catch let error as NSError {
        debugPrint(error)
    }
}


There is a catch (!) however: Existing objects already loaded into
the managed object context are not automatically removed, and
doing so it a bit tricky. See https://www.bignerdranch.com/blog/new-in-core-data-and-ios-8-batch-updating/ for more information.