Multi-walled carbon nanotubes (MWCNTs) underwent failure during crack opening in a MWCNT/alumina composite. Transmission electron microscope observations and single nanotube pullout tests revealed that the MWCNTs, rather than pulling out from the alumina matrix, broke in the outer shells and then the inner core was pulled away, leaving fragments of the outer shells in the matrix (i.e., they underwent failure in a "sword-in-sheath" fracture mode, as observed for MWCNTs under tensile loading). Some MWCNTs failed leaving either a very short sword-in-sheath failure or a clean break. Theoretical predictions based on the MWCNT failure and pullout models suggested that the use of MWCNTs having a much higher load carrying capacity may lead to composites with a higher fracture toughness. These results may provide new insight into the fracture mechanisms and suggest a new design methodology for MWCNT-based ceramic composites, leading to improved fracture toughness.