Mad Dummy is useful, but situational.
Although it only has 1 HP, it will not be killed off by any monster or effect card that does 3 damage or less. This also means that it can survive attacks from various spells such as Punishment and Undyne's Spears, making it quite effective as a damage sponge against Justice decks. And because it doesn't take damage from weak attacks, it also doesn't get KR while facing a Perseverance Deck, just like cards with Dodge, such as Sans and Sad Dragon.
Because of its price, it is also is decently effective in the Integrity deck, especially if placed early on against the opponent's weaker early game cards, or taunts like Jerry. Can be easily countered by silencing cards, and surprisingly well by Madjick.