What is the mechanism for deep-sea volcanism of the Gakkel Ridge in the Arctic? Related to an earlier question, What is the geochemical source for the helium detected in deep Arctic explosive eruptions?, where it is stated in the linked article that there is evidence of explosive volcanism deeper than 3km depth - the evidence coming from both seismic and petrological observations.  The article Hotbed of Volcanic Activity Found Beneath Arctic Ocean suggests that, as the article title alludes to, that the region has many hydrothermal vents and explosive centres.

These types of eruptions are not thought to be able to occur at depths greater than 3km, according to the article Arctic Volcanoes Found Active at Unprecedented Depths.

What is the mechanism for deep-sea explosive volcanism of the Gakkel Ridge in the Arctic?
There is some considerable uncertainty as the exact mechanisms. However, the recent seismicity and pyroclastic deposits detected around the ridge provide a unique opportunity to observe and model the baheviour of ultraslow spreading ridges.

According to the article Explosive volcanism on the ultraslow-spreading
Gakkel ridge, Arctic Ocean (Sohn et al. 2008), to overcome the pressure of the seawater, it becomes a question of the amount of volatiles (particularly $\ce{CO2}$ available in the magma chamber to cause fragmentation resulting in the glassy pyroclastic deposits observed around the volcanic centres on the Gakkel Ridge.

Sohn et al. hypothesise that the ultraslow spreading nature of the Gakkel Ridge would cause long intervals between volcanic events, which in the article, Effusive and explosive volcanism on the ultraslow-spreading Gakkel Ridge, 85°E (Pontbriand et al. 2012) suggest to be around 10,000 years. 

The long interval times allow for the accumulation of large volumes of volatiles in the upper part of the magma chambers. These would erupt periodically when the pressure in the magma chamber exceeds the deep sea-water pressure.  Models from Sohn et al. suggest that a weight fraction of 14% $\ce{CO2}$ (~75% volume fraction) would be required - a value considerably higher than those measured at most mid ocean ridges.  Pontbriand et al. estimate that $\ce{CO2}$ supersaturation in the magma chambers of the Gakkel Ridge to occur around 1500-2000 year timeframes (i.e. well within the estimated volcanism interval).

Pontbriand et al. go further and suggest that one of the most important implications of the observations (and modelling) of explosive volcanism on deep-sea ultraslow spreading ridges challenge the hypothesis that eruption volume varies inversely with mid ocean ridge spreading rates.