Which theory of aging suggests that mechanical functions of the body work less efficiently as people age?

It is the wear and tear theory of ageing.

The wear and tear theory defends that ageing is caused by the damage that happens as time goes by to cells and body systems. The name of the theory reflects this idea of wearing out - the organism is worn out and doesn't function normally. This is the theory that's accepted more generally as common sense but there are other theories of ageing that see the process as a more intentional process.