We introduce a new bio-inspired operation called a site-directed deletion motivated from site-directed mutagenesis performed by enzymatic activity of DNA polymerase: Given two strings x and y, a site-directed deletion partially deletes a substring of x guided by the string y that specifies which part of a substring can be deleted. We study a few decision problems with respect to the new operation and examine the closure properties of the (iterated) site-directed deletion operations. We, then, define a site-directed deletion-closed (and-free) language L and investigate its decidability properties when L is regular or context-free.