Top k values in each row of matrix excluding diagonal

You can use order :

diag(input_matrix) <- NA
k <- 2
t(apply(input_matrix, 1, function(x) 
        replace(x, -order(x, decreasing = TRUE)[1:k], 0)))

#      [,1] [,2] [,3] [,4]
#row1  0.00  0.2 0.28  0.0
#row2  0.20  0.0 0.00 -0.5
#row3  0.28  0.0 0.00  0.3
#row4 -0.11  0.0 0.30  0.0