There is only one reason why the tax multiplier is different from the spending multiplier. This is because the tax multiplier has one less “round” of impact on aggregate demand.
The spending multiplier works because the money that the government spends is then spent over and over again. It is first spent when the government pays someone for work that they have done. This increases demand for the first time. That person spends the money to buy goods, thus making a second round of demand using the same money. This process continues on through a number of rounds.
The tax multiplier works the same way, but it has one fewer rounds. When the government lowers taxes, it does not actually pay anyone. All it does is to refrain from taking money in taxes. Therefore, when a person spends what they have saved through a tax cut, that is the first round of increasing demand, not the second as it is when we are talking about government spending.