Is there a prohibition against gesturing with the hand towards body parts when explaining something bad, such as pointing to the wrist when mentioning the حد (prescribed punishment) for theft, or pointing to the neck when mentioning the method of slaughtering?

There is no harm in providing illustrative examples like these, and nothing has been reported to prohibit them. On the contrary, some Companions' actions indicate their permissibility, as Abu Lubabah (may Allah be pleased with him) did when he pointed to his throat, signifying the slaughter of Banu Qurayzah. As for the common saying regarding this, it does not validate a prohibition.