Is it permissible to rejoice at the martyrdom of someone at the hands of disbelievers, considering it a good thing for him, or does this nullify one's Islam?

Joy is dependent on its cause. Praiseworthy joy is that which stems from the attainment of something Allah loves and benefits His servants, such as a Muslim's joy at his Muslim brother achieving the rank of martyrdom in the cause of Allah, because martyrdom is among the highest stations with Allah.

As for blameworthy joy, it is that which stems from disobedience to Allah, such as rejoicing at the triumph of a disbeliever over a Muslim. Assisting disbelievers against Muslims out of love for them and a desire for their triumph is disbelief that expels one from the faith. However, if the assistance is for personal gain, out of fear, or due to worldly animosity, then it is forbidden and a major sin, but not disbelief.