Destroy period staircase heartlessly (5)
I believe the answer is:
erase
'destroy' is the definition.
(I've seen this before)
'period staircase heartlessly' is the wordplay.
'period' becomes 'era' (era is a kind of period).
'heartlessly' says to hollow out the word (remove centre letters).
'staircase' with its middle taken out is 'se'.
'era'+'se'='ERASE'
(Other definitions for erase that I've seen before include "Kill" , "Obliterate" , "Destroy recording on audio or video tape" , "Eradicate" , "Blank out" .)