Deficit: can be seen as a return? Suppose I have a series of debt as % of GDP.

By computing returns on this serie e.g.

debt as % of GDP in year 1 is 50% in year 2 is 60%

I compute $(60\%-50\%)/50\%$ can I interpret this measure as a sort of deficit for year 1-2? Hence, deficit for this period is 20%. Or shall it rather be the difference $10\%$?
None of these. Your measure is very different from the deficit. But, more generally, if this is all you know, you can't calculate it. You would also have to know GDP or the debt. Here is an example to show that it does not work:

+------+------+---------+------+-------------+--------------+
| YEAR |  GDP | Deficit | Debt | Debt to GDP | Your Measure |
+------+------+---------+------+-------------+--------------+
| 2011 |  100 |      10 |   10 | 10%         |              |
| 2012 |  110 |      12 |   22 | 20%         |            1 |
| 2013 |  120 |      14 |   36 | 30%         |          0.5 |
+------+------+---------+------+-------------+--------------+