Is it Russian Olive (fruits olive-like and thorny branches) or Autumn Olive (fruit a red drupe and "spur branches")?

Russian Olive - for trees, make stem injections using imazipyr (Arsenal AC) in dilutions (usually 20 percent) and cut-spacings (made with a hatchet, usually 1 "cut" per inch of d.b.h.) per the herbicide label. This can be done anytime but spring for best results. For seedlings and saplings, thoroughly wet all leaves with a 1 percent solution of imazipyr plus a surfactant (in water) during summer to fall. If there are desirable plants nearby, use a 2 percent solution of glyphosate (RoundUp). 

Note: Imazipyr is soil active, glyphosate is not. If safety to surrounding vegetation is important, use the glyphosate.

For more info on control of invasive plants, "google" or "bing" (don't want to show favorites) TreeSearch and look-up A Management Guide for Invasive Plants in Southern Forests, a.k.a. General Technical Report SRS-131. And for help in identifying invasives, A Field Guide for the Identification of Invasive Plants in Southern Forests, a.k.a. General Technical Report SRS-119.

Hope this helps!!