Here is one way to do that.
Please note that I could not use your reprex because I do not have access to the data you load with attach.big.matrix. There is no need to use your actual data in a reprex. A small example matrix is enough.
MAT <- matrix(c(0.1,0.2,0.3,0.4,1,2,3,4,0,0.4,0.5,0.6,4,5,6,7,0.2,0.3,NA,0.3),nrow=4)
MAT
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.1 1 0.0 4 0.2
#> [2,] 0.2 2 0.4 5 0.3
#> [3,] 0.3 3 0.5 6 NA
#> [4,] 0.4 4 0.6 7 0.3
MyFunc <- function(VEC) max(VEC, na.rm = TRUE) >= 1 | any(is.na(VEC))
BadCol <- apply(X = MAT, MARGIN = 2, MyFunc)
CleanMAT <- MAT[,!BadCol]
CleanMAT
#> [,1] [,2]
#> [1,] 0.1 0.0
#> [2,] 0.2 0.4
#> [3,] 0.3 0.5
#> [4,] 0.4 0.6
Created on 2020-10-31 by the reprex package (v0.3.0)