How can electric fields inhibit tumor growth?
In a PNAS paper by Palti's group (2007) they explain the hypothesis behind the technique:

They reason alternating currents of 100 kHz to 1 MHz specifically affects dividing cells and thereby targets cancer cells. Note that this is the same basic idea as chemotherapy and radiotherapy, which also target dividing cells mostly. The mechanism of action of alternating electric fields on dividing cells is though to be the result of a specific effect on the  bridge separating the daughter (cancer) cells during cell division (Fig. 1). They think it interferes with spindle tubulin orientation and induces electrophoretic effects (Kirson et al., 2007), resulting in a pile-up of cytoplasmatic organelles at the cleavage furrow. This is thought to interfere with cytokinesis, and to lead to cell destruction** (Kirson et al., 2004).  

Note it is the frequency that differentiates between the various effects of current stimuli. At very low frequencies (1 KHz) electric fields stimulate excitable tissues through membrane depolarization. At higher frequencies this excitatory effect is lost. At very high frequencies (>1 MHz) tissue heating results (e.g., microwave ovens).  Hence, alternating electric fields of intermediate frequencies (10 kHz to 1 MHz) were considered not to have any meaningful thermal effects (Kirson et al., 2004).


Fig. 1. Palti's electric field hypothesis. Source: Kirson et al. (2007)

References
- Kirson et al., Cancer Res (2004); 64: 3288-95
- Kirson et al., PNAS (2007); 104(24): 10152–57