In this work, we study the Biclique-Free Vertex Deletion problem: Given a graph G and integers k and i≤j, find a set of at most k vertices that intersects every (not necessarily induced) biclique Ki,j in G. This is a natural generalization of the Bounded-Degree Deletion problem, wherein one asks whether there is a set of at most k vertices whose deletion results in a graph of a given maximum degree r. The two problems coincide when i=1 and j=r+1. We show that Biclique-Free Vertex Deletion is fixed-parameter tractable with respect to k+d for the degeneracy d by developing a 2O(dk2)⋅nO(1)-time algorithm. We also show that it can be solved in 2O(fk)⋅nO(1) time for the feedback vertex number f when i≥2. In contrast, we find that it is W[1]-hard for the treedepth for any integer i≥1. Finally, we show that Biclique-Free Vertex Deletion has a polynomial kernel for every i≥1 when parameterized by the feedback edge number. Previously, for this parameter, its fixed-parameter tractability for i=1 was known (Betzler et al., 2012) but the existence of polynomial kernel was open.