The thing to remember about La Fille Mal Gardée is that there is more than one version. The ballet was originally written in the late 18th century by Jean Dauberval, and this version is still performed today; it is the basis of a version by the Basel Ballet that was recorded for German TV in the 1980s, and is currently available on video in Britain. This version has no spanking in it. The spanking has not been cut out: it was never there in the first place. In 1960 Fille was revived for the London Royal Ballet with new choreography by Sir Frederick Ashton, and this is the version which includes the spanking scene. It is part of the standard repertory of the Royal Ballet and has been produced in various other countries, including Denmark and Canada, but other versions are still around too. There are two different recordings available on DVD in Britain (the 1981 performance with Lesley Collier and the 2000 Australian Ballet one with Fiona Tonkin) but, if in doubt, the key thing is to ensure that you're buying the version with the Ashton choreography.
The basic story of the ballet is familiar enough. Lise (the naughty daughter of the title) and her mother have different ideas about her love-life: Lise wants to marry an attractive young man, but Widow Simone favours a rich, stupid one. Widow Simone throws out Lise's boyfriend and sets her to churning milk, but Lise disobeys and plays with her friends. Widow Simone returns, and Lise's attempts to hide are to no avail: she's caught, and her mother shoos away her friends. The Lesley Collier version is very good at this point, because Widow Simone basically gets hold of her by the skirt, so that Lise's attempts to get free result in a nice display of frilly-knickered bottom. Once the yard is clear, Lise is picked up bodily, carried across the stage horizontal with her legs waving attractively in the air, set on her feet and then turned across her mother's knee. The music builds up, the skirt is raised to reveal her panties. And then...
This is the moment to say that, for what it's worth, there's some evidence that the choreography has changed slightly over the years. It's at this point, with Lise over her mother's knee, that the Widow's preferred suitor and his wealthy father choose to arrive. What seems to change is whether the spanking has actually started by then. When the Widow sees her unexpected visitors, her arm is raised to smack Lise (and her open spanking hand promptly folds down and gives a comical little wave). But has she already struck by the time she is interrupted? In the earliest performances, apparently not: I have read a summary of the plot which says that she is 'about to administer a good spanking', and one eye-witness confirms that no smack landed. Not so in the Collier and Tonkin performances, though: there are two or three slaps for Collier and five for Tonkin before the other characters enter! But glad as I am of that, it's clear from the Tonkin performance in particular that this wasn't the effect that was originally intended. The phrasing of the music as Lise is put across the Widow's knee is building up to a climax: it's basically saying 'This is it, she's about to get the ultimate deterrent!' And then there's an immediate change of key as the visitors arrive, with no score covering the spanking itself: the climax doesn't happen, and Lise is fortuitously saved in the nick of time. The Tonkin performance gets in a relatively extended spanking before the interruption only by mismatching it with music that is (as I read it) building up to the spanking rather than scoring it.
The point of the scene, I think, is more the discomfiture of the Widow than the spanking of Lise as an end in itself. She's out to present Lise as an eligible fiancée for her rich neighbour's son, but she is also typically puritanical about youthful sexuality (which is why she chases Lise's boyfriend away). This is why it's important that Lise's skirt is raised for the spanking: Widow Simone is not just caught out as she's about to do (or actually doing) an undignified maternal duty, she also unwittingly shows off Lise's semi-clothed legs and bottom to male eyes. As the scene is blocked, it's always the back end of Lise that is facing towards the yard entrance when she's over her mother's knee, and the Widow's next action after the wave is to quickly pull down Lise's skirts and cover her up. In other words, it's a scene which wrong-foots the Widow's sense of propriety, and it's certainly not about embarrassing Lise, who is facing the wrong way to be able to see what is going on; Lesley Collier has an engaging 'What's happening now?' puzzled look on her face as she is allowed to get up from her spanking position.
I might add that the skirt is always raised. As well as the two recordings, there are at least two photographs of the spanking scene in existence, both with the skirt up. One of these shows Nerina in the first performance. Lise's exposed panties are actually part of the choreography!