Hello all! Brand new to this forum and to gardening, so please bear with me!

Our neighbours have a large tree (I THINK it's an elm tree, but I'm not sure) growing right alongside our fence. There are a few places where the tree roots are above the ground on our side of the fence, and these roots have sprouted new mini trees. Is there a way I can "neuter" the roots so they don't sprout, without killing the tree? The roots come up right around where I have flowers planted, so I don't want to damage my plants with any kind of chemicals or aggressive digging, if I can avoid it... If I saw the roots that are above ground off, will that kill the tree??

Any help would be greatly appreciated. I can't see my daffodils past the tree spouts!