There is a maple tree growing next to my house behind a large rose bush. I need to kill it so it does not ruin the foundation of my house.

How much time do you have?

You can girdle the tree close to the ground - that will disrupt the flow of nutrients up and down and the tree will die. You can hurry that process up by painting the trunk where you removed the bark with full strength brush killer.

But I would think that eventually, you would want to cut the tree down. You can cut the tree down and treat the stump with brush and stump killer (full strength). You want to coat the bark and the area just inside the bark. You don't need to paint the inner part of the tree stump as that part of the tree just holds the whole thing up.

Unless you want a dead tree next to your house for the next few years, until it decides to keel over (maybe onto your house!) you really do need to cut it down first.

Then do as Daisy suggests and paint the stump rim to keep it from putting up suckers - you may need to repeat the application of the brush and stump killer next spring, as the tree might be already going dormant now.

just saw around it -all the way around into the soft wood just under the bark. It will take a while for it to die. It will have to come out or it will eventually land on your house-or invite termites as it rots.

Its absence may also affect your foundation when the root mass rots and leaves a void.

best to cut tree down 1st. Low as can be. Then buy some stump killer. Its a powder that comes in a cardboard can. Follow directions and it works!!! And Hopefully.all the roots that may want to send up sprouts. If any suckers come up. Dig to root.drill holes in root. Not through root. And pour straight round up type product in holes.
Dont do this if edible plants are close by. 😬

well we don't know how big the tree is?

Yes, please, what size is the tree? Diameter of the main trunk? Height of the tree? That would help to know if it would require a professional tree removal service or if you can take it down yourself. I usually take down trees by myself or with one helper to hold the rope but once I paid $900 for a really large oak tree in a precarious location. Better to have a professional tree service with insurance for a big job.

No matter what size the tree is, it is easier to cut fresh wood than to cut dead wood. Also, the dead tree is a hazard to persons and property. Best to cut the tree down while it is alive.

As several have noted above, a slowly dying tree is as bad as a growing one. It isn't just the top part you affect- it's also roots which can be heaving your foundation up, or will cause a cave in when gone. As a tree dies, it can drop limbs - or rather branches. Roundup brush killer and salt are both used to kill stumps by applying into drilled holes. Roundup stays in the ground so care must be taken. You didn't indicate the size of the tree, but removal of smaller limbs can damage rooftops just as limb drop can. So, costs must be evaluated in case of worst case scenarios. Good luck

If your tree is at a safe distance, Philip's advice will work. I have done almost exactly what @Philipwonal described for you. I used stump remover powder, drilled a ton of holes as deep as I could get them in the stump, and filled with the remover. The Roundup in roots if suckers pop up is an excellent suggestion I wish I had thought of. Over the winter, I kept the stump constantly wet, to encourage the stump to rot a bit. I replaced the stump powder a few times too. With a bit of whacking away with a big awl, we removed it without breaking our backs. Good Luck!