Can a proton be ejected from an atom?
Is it possible to remove a proton from the atom via some technique
  such as bombardment with another particle or applying an appropriate
  amount of energy to the system?


Yes, this occurs in nature and can also be done in the laboratory.  In nature the process is known as radioactive decay.  Listed below are two decay processes that will remove a proton(s)


alpha decay: an atom ejects a helium nucleus (2 protons and 2 neutrons) 
$$\ce{^239_94Pu -&gt; ^4_2He + ^235_92U}$$
beta-plus decay: a positron is emitted and a proton is converted to a neutron.


In the (nuclear) lab, a process known as phototransmutation can be employed.  If a nucleus is irradiated with high-energy gamma rays (high-energy photons) it can absorb the energy and change to another element by ejecting a proton and\or neutron
$$\ce{^25_12Mg -&gt;C[{h\nu}]\   ^1_1H + ^24_11Na}$$

You can make a rough estimate of the energy required as follows:
$$\mathrm{24.98583692\,amu~ \longrightarrow 1.00727647\,amu + 23.99096278\,amu}$$
comparing the starting and final mass, we find that 0.01240233 amu has been gained in the process.  Since 1 amu = 931.5 MeV, the gamma ray photon would have to have an energy of at least 11.6 MeV.