I live in St Paul mn zone 4 can I grow sweet potato on a teepee

Sure, if you're just interested in growing it for the nice foliage - there are decorative types with dark red, and also chartreuse green foliage that are really pretty. Your growing season up there in MN isn't nearly long enough for you to actually harvest sweet potatoes.

I asked Baker Creek just to be sure

I tried growing sweet potato last summer here,--- in what was zone 3,
and now we are the Canadian zone 4a .
I did not get roots worth harvesting.
I am going to try again this year,
-- using a sort of green house made from a glass patio table.
It will be skirted in to make it humid.
My plants were damaged last year by hail.
I tried using a variety called Covington.
There are some short season varieties that have been developed.

I'll look into it more hope it works

A friend of mine gets an abundant harvest of large sweet potatoes every year in zone 5a, so I would think you could grow them in zone 4 under the right conditions. He is somewhat limited in the varieties he can grow, though, with the most success coming from Georgia Jet and Centennial. You'll want to plant them where they get the maximum amount of sun and heat and rich, but light, soil helps as well.

In "pushing the zones" we have to remember the zones are devised from lowest winter temperatures predominantly. That is useful for growing perennials.
For growing summer vegetables it is the length of the growing season which is more important than zones.
By using various season extending measures, we can grow over longer time than our average
number of grow days.
And of course----it all depends on the weather in any particular summer!
Gardening is always a gamble on weather ! So we work with whatever comes!

Georgia Jet is a short season variety which is recommended for growing up here.
I could not get it last year.

Okay thanks I will look into it next year