I have a Path that must resize to its StackPanel container.
Ensure that your path is smaller than your StackPanel.
Easiest way for a very easy path will be to move the comma in every number (i.e. divide everything by 10 or 100 in TranslateZ), or for more complicated paths add a LayoutTransform (lower the scaling factor as needed):
Some Remarks:
I had a similar problem, with a button template containing a path. The button's "auto" size was determined by the path, because the path had the largest dimensions of the template content.
This in itself might not turn out as a problem, because if you specify the button's height/width, or if the button's Horizontal-/VerticalAlignment is set to stretch, of course the path will scale.
For other values of Horizontal-/VerticalAlignment however, the button size gets determined by the amount of space required by its content, which in my case resulted in a button with the path's original dimensions.