This study investigates the stirring of the thermohaline anomalies in a fully turbulent quasigeostrophic stratified flow. Temperature and salinity fields are permanently forced at large scales and are related to density by a linear equation of state. We show, using some inherent properties of quasi-geostrophic turbulence, that the 3-D ageostrophic circulation is the key dynamical characteristic that governs the strength and the spatial distribution of small-scale thermohaline fronts that are strongly density compensated. The numerical simulations well illustrate the formation by the mesoscale eddy field of sharp thermohaline fronts that are mainly located in the saddle regions and around the eddy cores and have a weak signature on the density field. One important aspect revealed by the numerical results is that the thermohaline anomalies experience not only a direct horizontal cascade but also a significant vertical cascade. One consequence of this 3-D cascade is that the ultimate mixing of the thermohaline anomalies will not be necessarily maximum at the depth where the large-scale temperature and salinity anomalies are maximum. Some analytical arguments allow us to identify some of the mechanisms that drive this 3-D cascade.