The slip and stick of soft permeable particles sliding near a smooth surface is determined by computing flow, pressure and shape of a particle pressed against a surface due to the osmotic pressure of the surrounding suspension and its translation at constant velocity parallel to the surface. We present a poro-elastohydrodynamic lubrication theory that accounts for the interplay of the viscous pressure force on the elastic deformation of the particle and the flow through the particle pores. At high particle velocities, the particles move along an elastohydrodynamic film of fluid causing the particles to slip on the surface. For finite particle permeability, there is a critical particle velocity determined by the permeability relative to the thickness of the film and a ratio of the viscous and elastic forces that cause a portion of the particle to contact the surface and stick. In this case the magnitude of pressure in the lubricated film is lower compared to their impermeable counterpart sliding against a smooth surface at the same speed. The particle pores offer an alternative route for the fluid in the film, reducing the lubrication pressure resulting in the particle contacting the surface. A universal function is deduced to predict this transition for a range of poro-elastohydrodynamic interactions. The drag force of the particle sliding along the surface up to the contact is also determined and found to follow a universal function. These results demonstrate the possibility of dynamic stick-slip transitions via control of particle properties instead of wall surface treatments.