DSPs have different memory architecture. MC most often use shared program and data memory, whereas a 56k uses a super harvard architecture with separate program and data memory. The 56k for example has a program and 2 data memories internally which all can be accessed at the same time. This way DSP algorithms can be executed much faster, since two operants and the next instruction can be fetched within one clock cycle.
The ALU is a bit different. Most DSP use fixed point now and offer saturation and speical rounding modes, which are usually needed for DSP algorithms.
DSPs do not have a MMU, but in the case of a 56k they have special addressing modes, as for example automatic wrapping and special modulo modes, which match nicely with DSP algorithms.
HTH.