We report on the successful operation of a newly developed cryogenic jet target at high intensity laser-irradiation. Using the frequency-doubled Titan short pulse laser system at Jupiter Laser Facility, Lawrence Livermore National Laboratory, we demonstrate the generation of a pure proton beam a with maximum energy of 2 MeV. Furthermore, we record a quasi-monoenergetic peak at 1.1 MeV in the proton spectrum emitted in the laser forward direction suggesting an alternative acceleration mechanism. Using a solid-density mixed hydrogen-deuterium target, we are also able to produce pure proton-deuteron ion beams. With its high purity, limited size, near-critical density, and high-repetition rate capability, this target is promising for future applications.