Looks like a Pyracantha to me but difficult to tell without seeing a photo of the whole shrub. If you don't like it simply dig it out including all the roots.

Is it still oozing sap at this time of year? Agree a photo of the whole shrub would help with identification.

It's not a Pyracantha--the thorn structure isn't right. Right now, I'm thinking a barberry, maybe Berberis vulgaris?

Those thorns in 3's do make it a Berberis.

The yellow sap made me think of Berberis as the ones we have all leak yellow sap when cut.

Sorry, forgot that Berberis have rather large thorns too! You're right...

Re getting rid of it, get yourself some good thorn proof gloves. Then the easiest way would be to cut it down, removing the branches first, leaving a stump a couple of feet high with no branches (or thorns!) Then its a matter of digging round it, sawing off the roots and using the stump as a lever to work it loose and pull it out. (Not speaking from theory, we have done it) Dig out as many of the big roots as you have energy for afterwards, but they will rot down eventually if you feel this is too much..
Have fun!