We study the base pairing dynamics of DNA with repetitive sequences where local strand slippage can create, annihilate, and move bulge loops. Using an explicit theoretical model, we find a rich dynamical behavior as a function of an applied shear force f: reptationlike dynamics at f=f(c) with a rupture time tau scaling as N3 with its length N, drift-diffusion dynamics for f(c)<f<f(*), and a dynamical transition to an unraveling mode of strand separation at f=f(*). We predict a viscoelastic behavior for periodic DNA with time and force scales that can be programmed into its sequence.