I've served half a month in an organization and resigned. The organization has deducted full tax for the month (that is tax on full month salary). Is this right? Shouldn't the tax be deducted on the income earned for that month, which is half a month salary?

You are correct.

Tax deductions are always based on the taxable gross amount of the check. What makes you think they withheld for more? Have you checked withholding tables?

In any event, if you were over withheld, you will get it back when you file your return.

I did payroll years ago, and often took over for someone who had no idea what they were doing, so I can believe this in a small company who doesn't use a payroll service.