Relationship between toxicity of drugs and negative effects on brain
Short answer
The causes of death after heroin, cocain or cannabis overdose are mainly due to cardiac and respiratory arrest, and not to neurotoxic effects. 

Background
The cause of death after a lethal overdose of your mentioned drugs are the following :


Cocaine (lethal dose: 30 mg - 5 g via mucus membrane (EMCDDA)): Cocaine-related deaths are often a result of cardiac arrest followed by an arrest of breathing (NIH). Cardiac effects are mediated via increased sympathetic output and a local anesthetic effect (Schwartz et al., 2010); 
THC: (lethal dose: ~1000mg/kg i.v. in primates (Drug library)): No known cases of human fatalities. Toxicity appears as achypnea (rapid breathing), tachycardia (fast heart rate), ataxia, hyperexcitability, and seizures (Fitzgerald et al., 2013), but death seems mostly associated with respiratory arrest and cardiac failure (Drug library); 
Heroin: (lethal dose 200 - 2000 mg i.v.(EMCDDA)): overdose often due to respiratory arrest (Anoro et al. 2004) caused by mu-opiate receptor activation in the brainstem (Karch, 2006). 


Hence, heroin, THC and cocain are lethal mainly due to peripheral causes (i.e., cardiac and respiratory arrest). Although these effects are mediated, at least partly, through central mechanisms (i.e., occurring in the central nervous system and specifically the brain), the drugs themselves do not cause death because of neurotoxicity. 

And a closing comment, with credits to @MarchHo - In general, neurotoxins do not cause death due to neural toxicity per se. Most notably even botulotoxin, being one of the most potent neurotoxins known, causes death due to respiratory failure (CDC).

References
- Anorro et al., Rev Esp Salud Publica (2004); 78(5): 601-8
- Fitzgerald et al., Top Companion Anim Med (2013); 28(1):8-12
- Karch, Drug Abuse Handbook (2006) 
- Schwartz et al., Circulation (2010); 122:2558-69