The reason for this is that the spending multiplier gets spent one more time than the tax multiplier does.

If the government pays me $1000 to do something for them, that $1000 goes on GDP.  And then I spend some amount of it.  And the person who I pay spends some amount of that, and so on.  That's the multiplier, right?

Well, if the government lowers my taxes by $1000, that act of lowering my taxes does not increase GDP. So the first step I described above does not happen. Instead of getting money from the government, I just don't have to pay money.

So when the government pays me to do something, GDP goes up.  When it refrains from taking my money, GDP does not go up.

That's why the spending multiplier is higher.