There are two shortcuts in Twisted Mansion, one at the start and the other at the end of the lap. Both cut out a small section of the track, but if you look at our video below, the shortcut exploited at the beginning of the track yields the fastest time (it's even against the previous video's ghost, so you can easily compare the times).
The reason for this is that, on some laps, you can cut the final corner under the automated hammer, lessening the effectiveness of cutting across the grass. You may find on some races that using the latter shortcut is more effective, try both and see which one is most effective, or even mix and match.
Although Twisted Mansion has a wide track, drifting on straights will cost you overall. Equally, try and glide as straight as possible in the garden - hopefully the Boos won't get in your way too much and you'll end up back in the mansion without too much trouble. Always try and land on the upper tier, as going up the stairs is slower.