Disk galaxies at high redshift (z ∼ 2) are characterized by high fractions of cold gas, strong turbulence, and giant star-forming clumps.Major mergers of disk galaxies at high redshift should then generally involve such turbulent clumpy disks. Merger simulations, however, model the ISM as a stable, homogeneous, and thermally pressurized medium. We present the first merger simulations with high fractions of cold, turbulent, and clumpy gas. We discuss the major new features of these models compared to models where the gas is artificially stabilized and warmed. Gas turbulence, which is already strong in high-redshift disks, is further enhanced in mergers. Some phases are dispersion-dominated, with most of the gas kinetic energy in the form of velocity dispersion and very chaotic velocity fields, unlike merger models using a thermally stabilized gas. These mergers can reach very high star formation rates, and have multi-component gas spectra consistent with SubMillimeter Galaxies. Major mergers with high fractions of cold turbulent gas are also characterized by highly dissipative gas collapse to the center of mass, with the stellar component following in a global contraction. The final galaxies are early-type with relatively small radii and high Sersic indices, like high-redshift compact spheroids. The mass fraction in a disk component that survives or re-forms after a merger is severely reduced compared to models with stabilized gas, and the formation of a massive disk component would require significant accretion of external baryons afterwards. Mergers thus appear to destroy extended disks even when the gas fraction is high, and this lends further support to smooth infall as the main formation mechanism for massive disk galaxies.