Swift observations suggest that the central compact objects of some gamma-ray bursts (GRBs) could be newly born millisecond magnetars. Therefore, by considering the spin evolution of the magnetars against r-mode instability, we investigate the role of the magnetars in GRB X-ray afterglow emission. Besides modifying the conventional energy injection model, we pay particular attention to the internal X-ray afterglow emission, whose luminosity is assumed to track the magnetic dipole luminosity of the magentars with a certain fraction. Following a comparison between the model and some selected observational samples, we suggest that some so-called "canonical" X-ray afterglows including the shallow decay, normal decay, and steeper-than-normal decay phases could be internally produced by the magnetars (possibly through some internal dissipations of the magnetar winds), while the (energized) external shocks are associated with another type of X-ray afterglows. If this is true, from those internal X-ray afterglows, we can further determine the magnetic field strengths and the initial spin periods of the corresponding magnetars. Comment: 10 pages, 5 figures, accepted for publication in ApJ