Delete Method in Axios, Laravel and VueJS

It is because of the method signatures. The default delete route when using Resource expects a single parameter. So when doing:

axios.delete('api/users', {params: {'id': this.checkedNames})

you are missing a required parameter. The route definition is

Route::delete('api/users/{id}', 'UserController@destroy');
// You are missing `id` here. So it won't work. 

Usually, if you are going to stray away from the default behavior, it is recommended to create your own function. So you could leave the default destroy($id) function as is to delete a single entry and write a new function that will delete many. Start by adding a route for it

Route::delete('api/users', 'UserController@deleteMany');

Then define the function to handle it

public function deleteMany(Request $request)
{
    try 
    {
        User::whereIn('id', $request->id)->delete(); // $request->id MUST be an array
        return response()->json('users deleted');
    }

    catch (Exception $e) {
        return response()->json($e->getMessage(), 500);
    }
}

To summarise, your problem came from route definition. Your route from Axios did not match the route definition from Laravel, hence the 405.

I also experienced the same problem. This works for me:

deletePost: function(id) {
                axios.post('/posts/'+id,{_method: 'delete'})
            }

Using axios.post() instead of axios.delete, and sending _method "delete"