You need to get current image path of user before updating it with new one. So that you can use that old path to delete image file.

namespace App\Http\Controllers;

use Illuminate\Http\Request;
use Illuminate\Support\Facades\Auth;
use Illuminate\Support\Facades\DB;

class ProfileController extends Controller
{
    public function index($slug){

        return view('profile.index')->with('data', Auth::user()->profile);
    }


    public function uploadPhoto(Request $request) {

// Uplaod new image
$file = $request->file('pic');
$filename = $file->getClientOriginalName();
$path = 'storage/img';
$file->move($path, $filename);
$user_id = Auth::user()->id;


// Get current image of user, then delete it
$user = User::find(Auth::user()->id);
File::delete($user->pic);


// Then update profile picture column in database
DB::table('users')->where('id',$user_id)->update(['pic' =>$filename]);

return redirect('/editProfile')->withSuccess('Your image was successful.');

}

Before update you can access to old pic with

Auth::user()->pic