When governments reduce tax - both personal and business tax, families and businesses have more money to spend. If they spend money, economic grows. But two important issues arise:
(1) What if the families and businesses do not spend, but rather hoard or pay off debt:
Then, the money not collected in taxes would not circulate to the market to spur growth. This is exactly what happened during 2008 tax rebate program in United Sates.
(2) What do the governments do that rely on tax revenue as source of income?
It does place burden on governments. But, governments happen to gain from sales tax and other fees instead from payroll tax.
If government encounter budget deficit, it can borrow. Deficit will have impact on currency, inflation and interest rate in the long run.