Scandalous simply means to cause a scandal. You can use it as an expression of emotion after hearing something and say 'Scandalous!' or 'That's scandalous', the same as you might with 'that's a scandal!' But you can also use it sarcastically. I've never heard it used interchangeably with 'shame on you!'

Use "shame on you" if you want to tease someone. Scandalous is an adjective word to use in a sentence, for an example; "You had a scandalous affair!" or "What scandalous affair?"