I could not, under any fucking circumstances, dismember myself in any way shape or form. Be it slicing off a toe, or my whole lower leg. Neither would I kill myself via. asphyxiation. I don't think there's any amount of desperation that could make me willingly want to do those things, though I've never been pushed that far.
In the first situation, I'd probably down the alcohol and break the glass, puncturing the appropriate places in my throat and bleeding out until death.
In the second, I'd attempt to kill the shit out of my partner, and live off of him for as long as possible, using his body to lure fish, yet should they not come, I'd eat him. If I lost, then I'd have no choice but to die. Chances are if this person was harder than me I'd attempt to bludgeon him to death whilst he sleeps with a large stick.