Gramps has some support for mixed-style dates: see wikipedia.
It is best in your research to convert the date to something more usable before entering it in Gramps. That is, a mixed date is a mixing of Julian and Gregorian calendar, so errors may be easily made.
Eg, the example 11 February 1731/32 means the Julian year is 1731 and the Gregorian year 1732. However, this leaves the date 11 February dubious. Is it the Julian or the Gregorian date?
For matches, Gramps will interpret this date as Gregorian: 11 February 1732.
Conclusion: Gramps supports the input of the mixed-style date, but your research will be more reliable if you avoid it, and use the date editor to input Julian dates if you know the date is Julian (and use the editor to correctly convert to Gregorian if you want that), or use the normal Gregorian date in the date field.