I've got a wood stove in my daughters house that was installed in 1977. It is a free standing stove with exposed chimney to the ceiling. It still has a good draw but it will sometimes exhaust smoke from the joints of the metal chimney pipes. Is there any was to fix this (high temp caulk/epoxy) or do I need to pull the whole thing and have it redone?

I'm a little confused with your description , but I confuse easy, LOL. However, if it's standard metal stove pipe that's been there since 1977, I'd replace it all.

I have 0.00% experience with wood stoves but seems like high temp rated aluminum tape would work well.

If it's old stove pipe with a new problem it need to be replaced.

I'd replace the pipe rather than chase issues. Course I'm no mechanical but '77 was a while back.

Its just a wood stove with standard metal piping. Nothing fancy. I think its probably 10" diameter, 3' sections and look like they just slip together. Years ago someone (I'm guessing my father) put some kind of sealant on 2 of the bottom joints and now most of it has separated from the piping and will just pop off if you flick it. She tried to light a fire the other morning and it smoked up pretty good in the house when it started dying out. Lack of draw I guess.
I was hoping for a reasonable fix before winter but I just told her not to use it anymore until I can do something with it. May be a while before I can afford to get it rebuilt though. Almost $19,000 in her plumbing has set my home repair budget back a little.

I’m no Expert by any means, so don’t bet the Farm own my comments. I’ve actually been pondering starting a project building a couple. In my research I have found that 6” diameter draws the best, when it comes to Stove Pipe. Maybe someone else knows better, and can Chime in. Good Luck with your Project. 👍

Interior stove pipe is cheap. It's the triple wall stuff that's expensive.

You need double wall going from the stove to a ceiling box, then triple wall out the roof to about 2’-3’ above the ridge line.
That should take care of any draft issues. If the pipe is 10” diameter coming from the stove it may be already be double wall.
You have to use the size pipe the the stove uses, either 6” or 8”. My Buck stove uses 8” but it’s a large stove.

Why double wall inside?

I like it because it’s another layer of pipe/safety.
Doesn’t get near as hot on the outside of the pipe.
Probably not a necessity unless there’s some code for it but my preference.

That stuff he put in the joints was chimney cement. It is a little like cement and seals well, when new. Comes in a small plastic container. It is sort of like plumbers putty, if you keep it awhile it will get hard and crumbly.

If you want the most heat then use single wall from the stove to the ceiling box. Then use double or triple wall depending on clearece from combustibles.