Yes and no.
Let's assume that the property currently have a small amount of mortgage A. If you have the property rented out, yes, the interest you paid for the mortgage can be deduced for the rental income.
Now imagine that you went to a bank and had the mortgage refinanced to the new amount of B (B>A usually). The interest paid up to the previous amount of A is still qualified for income deduction. But the interest paid for the remainder B-A will depend on how you use the money. If you put the B-A inwards a new house down payment for your own live, you can not deduct this part of interest from the rental income. Or you use the money to buy the second rental property, the interest can be deducted form your second property rental income.
Refinancing is just another way to borrow money, and the difference from other means is that your borrowing is financially backed by your property, which make the deal go through much easily.