I understand that the budget has cut direct taxes for individuals but is it true that exemptions will not be available now?

You are right that the direct taxes will now have two different regimes simultaneously and you can opt for one of them. Firstly, you can choose the existing regime in which you can get all the exemptions and you pay tax at the old rates. Alternatively, you can choose the second regime where you pay lower tax but you lose all tax exemptions of Section 80C and Section 80D except for the benefits of provident funds. You need to calculate which regime is more profitable for you.

A quick analysis shows that the new regime is only beneficial if you are in the income group of 12 lakhs to 15 lakhs, not otherwise. For most off the other income groups, the new regime is less profitable compared to the old regime. The only advantage in the new regime is that it does not have any exemptions and hence all your income tax paid data will come pre-filled when you file returns, reducing your task substantially.