It certainly will affect everything
growing there as the pine
tree will absorb much of the water and nutrients from the soil where the roots are. Your
plants will be competing with the
tree for needed nutrients and water.
tree roots extend out as much as three times farther then the diameter of the
tree's dripline. They really don't have a "taproot". Most
plants don't. Their root systems are located
mostly in the top couple feet of soil where most of the water and nutrients come from. You really won't hurt a mature
tree by taking out some of the roots, but the
tree will relentlessly continue to send roots out into your planting bed. When a root is cut, say with a shovel, it will begin to branch out at the cut.
This is not to say that your
plants cannot sustain themselves in the shadow of a large
tree. The
tree will not take ALL nutrients, but you can make it easier on them by making up for the lack of nutrients with more fertilizer or compost.