The tree is totally normal, but there was a large branch cut off a long time ago because it was blocking the sidewalk. A small branch is growing out of that cut stump and all those leaves have the left half lobed and the right half toothed. No idea if its a graft, or just natural.
Is this a mulberry? It looks to me like a plant sport which is a variation arising from a single plant that differs genetically from the parent plant, it is essentially a mutation that manifests as a noticeable change in a plant’s characteristics, it can sometimes happen when the cellular structure has been messed with (say cutting off a limb) and the dormant buds grow and divide in differing ways giving the variation in the leaf characteristics. It’s just a guess though.
I agree, looks like a mulberry. Leaves on small trees and new branches are particularly likely to be lobed in mulberry, while older branches tend to produce leaves without lobes.