The Tree - to keep or not to keep

Actually I am not even sure that this tree is alive - it appears to have some buds in it, but from what I remember I am sure that it was bare back in August when we first viewed the house.
My Dad will have to come and have a look as I am pretty sure it has to go, also below the tree appears to be a animals grave - it's a small patch with no grass and it has some white wire around it - I am not a good gardener but I do want a garden that I can sit in and enjoy (and take photos of )
Well, we will see and I will keep you updated on the status of the tree!