Can't kill Sim by overexertion

@PicantePants818 if you just have ageing on in your Game Options they will die of old age. That will definitely kill them.

Game deaths are quite random. I rarely play with death or ageing on but I sometimes have them for storytelling purposes. I found it difficult to force it other than by causing a fire. I had one Sim who had no climbing skill on a mountain expedition which is where I wanted to kill him off. In the end I turned on Temperature Effects on Sims and got him to roll around in the snow in summer clothes. That worked. I kept trying to get him to fall from the mountain but he wouldn't, yet his partner with max climbing skill did. Luckily I back up my game and got her back and tried again. So I'd recommend the same, having a backup incase it doesn't work the way you want it to at first.

Hm... Indeed... I do wish that they'd add a cheat to age sims up so we can have elders die by old age whenever we want (right now mods are needed to unlock all cheats)... For now, you need Paranormal stuff pack to speed the aging bar up (sell soul to spirits).

Anyway, on overexertion.

There are three main ways to cause death by it:

• Exercise: This is the hardest to achieve as the moodlet that comes from Dangerously Tired gives 40 Uncomfortable points, disabling any exercising interactions. You'll need something strong to counter that. Something like an emotion potion from the Rewards Store. For just 200 Satisfaction Points, you can get 100 points to any positive emotion (except Playful) for 4 hours, countering the Uncomfortable moodlet just fine.
• WooHoo: No Uncomfortable moodlet will block this one out! The only thing you need there is a lover though...
• Research Machine: If you have Discover University and at least 5 levels in Research & Debate skill, contributing too much knowledge to the research machine can kill any sim by overexertion (even younger sims!).

These are my suggestions for now.

@PicantePants818 

There are several pretty easy ways to kill a sim.  

If you only have base game, the easiest way is to get them playful and then hysterical.  Hysterical deaths are the easiest of all.  Just have the sim start telling jokes, one after the other.  It won't take long.  Only problem with this way is that you could kill the sim they are telling the jokes to as well so it's best to have the sim tell jokes to several other sims, not just one.  

If you have a pool, have them keep swimming if exhausted.  Usually, they'll drown.

If you have a sauna, you can keep them going back in after they get overheated.  Although with some sims, you lose the options to make them go back in just like what happens with exercise equipment.

If you have Seasons, have another sim make a death scented bouquet on the flower table and gift it to the sim you want dead. Guaranteed to work every time.  What the bouquet does is cause the recipient to age up to the next life stage so for elders, it kills them.  If you have weather on, you can send them outside to try and get them hit by lightning but it might take getting struck more than once before it kills them.

If you have Tiny Living, a murphy bed that isn't upgraded will kill a sim if you keep them raising or lowering it for a while.

If you have Island Living, send them out to the diving buoy and make them keep diving after they get fatigued.  They can drown from overexertion, a shark might pull them under, or they get caught in a rip tide and drown.

If you have Discover University, sims can get shocked working on the robotics workstation.  After they've been shocked once, keep them at it and the next time they get shocked will kill them most of the time.

These are only a few ways to get a sim to die.  There are other ways in other packs not mentioned.

Hope this helps.

I've had drowning deaths recently and @CGrant56 's post has just reminded me of that. Mine were accidental and I reverted to my backup save as I didn't want them to die. I recall trying to get a Sim eaten by a shark just to see what happened but there was no "Jaws" moment which disappointed me. I don't think I knew they could drown while diving at the buoy so I'd better stop pushing my poor diving Sims so as to avoid an unwanted fatality! I didn't know about the sauna either.

Then there's starvation deaths too but they complain so much it requires turning down the volume!

I did end up building an in-law drowning shed, for the record, but I'd already accidentally exploded someone else's heart before that when he kept barging in on his husband trying for a baby with his girlfriend three times in a row, which seemed like a glitch of its own, the game decided no more sneaking around, I guess. I got the Grim Reaper to bring him back to life, then the revenant and death were chilling watching TV afterwards trying to get him to calm down, then one of the husband's hetero spawn interrupted to ask him for help potty training and he had another heart attack and I figured he'd prefer staying dead. The toddler didn't make it to the potty after witnessing a soul reaping. Worth it.