Wood stove flue leaking water at wall penetration
If the pipe you ran on the outside of your house is single wall stainless steel and you are using the wood stove with a minimum combustion air or the outside temp is fairly cold the water could be from the flue gasses condensing and running down the inside of the pipe. You could also be condensing the flue gasses and the water gets into the inside through a pipe seam. Post a picture of flue pipe so we can get a good look at it. I hope that you used a good wall thimble or left a lot of distance from the flue pipe to any combustible material when you exited the outside wall of the house. There could also be other reasons for your problem.