We introduce and study the Bicolored P3 Deletion problem defined as follows. The input is a graph G=(V,E) where the edge set E is partitioned into a set Er of red edges and a set Eb of blue edges. The question is whether we can delete at most k edges such that G does not contain a bicolored P3 as an induced subgraph. Here, a bicolored P3 is a path on three vertices with one blue and one red edge. We show that Bicolored P3 Deletion is NP-hard and cannot be solved in 2o(|V|+|E|) time on bounded-degree graphs if the ETH is true. Then, we show that Bicolored P3 Deletion is polynomial-time solvable when G does not contain a bicolored K3, that is, a triangle with edges of both colors. Moreover, we provide a polynomial-time algorithm for the case that G contains no blue P3, red P3, blue K3, and red K3. Finally, we show that Bicolored P3 Deletion can be solved in O(1.84k⋅|V|⋅|E|) time and that it admits a kernel with O(kΔmin vertices, where \Delta is the maximum degree of G.