Recently purchased this home which had empty garden beds in front yard. Have found some sprouting stems resembling some sort of shrub with shiny green leaves. Have just been removing these over last two years we've owned the home.

Would like to finally fill in the garden beds and purchased two Prairie Fire Dogwood plants. Wanted to plant near where the stems have been coming up, began digging and found a huge root right below the surface of the Earth where the stems have apparently been popping up from. Assuming it is a tap root...
Looked up an old Google street view image of our home and found this. The red arrow points to the plant in question.

How on Earth do we get this big root out? I'd like to remove it so the dogwood can have room to thrive.

I've read tips using stump killer and Round Up, but I need it actually out so that we can plant the dogwood. I've dug a trench around it trying to find some leverage and I am not having any luck.