What is the maximum cap for tax reduction for donations to charities? I know you can’t just donate to any charities, only government approved charitable agency that allows you to reduce tax

There is no cap on donation tax relief. You can donate a million dollars and get 2.5 million in tax relief.

No catch. The govt just wants more rich people to donate.

The tax reduction does not work like per your interpretation. It is not a direct tax reduction on your outstanding tax.

It will provide a deduction of your assessable income for tax instead like your other expenses.

eg on IRAS website
Example: Donation of $10,000 to an approved IPC

If your total statutory income for YA 2019 is $100,000 (i.e. you earned $100,000 in 2018) and you donated $10,000 to an IPC in 2018, your assessable income would be calculated as follows:

Total Statutory Income$100,000

Amount of Donation$10,000

Amount of Deductible Donations$25,000  ($10,000 x 2.5)

Assessable Income for YA 2019= $75,000 ($100,000 - $25,000)

As above you will still be taxed on the assessable income of 75k.

Given another scenario,

Example: Donation of $40,000 to an approved IPC

If your total statutory income for YA 2019 is $100,000 (i.e. you earned $100,000 in 2018) and you donated $40,000 to an IPC in 2018, your assessable income would be calculated as follows:

Total Statutory Income$100,000

Amount of Donation$40,000

Amount of Deductible Donations$100,000  ($100,000 x 2.5)

HOWEVER there is a max income tax relief cap of $80,000.

Hence the Real Amount of Deductible Donations is $80,000

Assessable Income for YA 2019= $20,000 ($100,000 - $80,000)

Luckily in this case, the first 20k are income tax exempt under the tiered assessment.