Your plant looks like Prunus virginiana.  Wild chokecherry.  To control this plant you can cut down the main tree at ground level and immediately apply a broad leaf herbicide or brush killer to the fresh stump.  The suckers can be cut off also at ground level and the weed killer/brush killer applied to each fresh cut. You may also want to put a coffee can or bucket over the main cut stump so that sprouts that appear will grow under the bucket and  be deprived of light.  Continue to cut any remaining suckers that appear and brush the new cuts with the herbicide. Because there will be much energy stored in the root system you may need to do this over a few seasons, but eventually enough of the herbicide will be brought down into the roots to kill the entire shrub. Remember too that the soil may contain numerous berries from previous years or even berries brought in by the birds this year so disturbing the soil as little as possible will prevent many of these berries from sprouting and creating new plants. Thank you for asking the eXtension site your question.