If you apply enough force, yes. Fortunately, a human with a sharp object can not apply enough force.
Atoms are made up of electrons, protons, and neutrons.
Atoms connect to other atoms by bonds in the electrons. When you cut, for example paper, you are breaking the bonds between the electrons.
Electrons can not be cut in half because they are elementary particles. There is nothing that makes them up.
Protons and neutrons on the other hand, CAN be “cut”. They are made up of quarks. However, to do so, requires an enormous amount of energy.
This is why we have particle accelerators such as the large hadron collider. They get a particle moving extremely fast and smash it into something like a proton to “cut it in half”.
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