x <- gsub("'", "", x)
x <- gsub(" ", "_", x)

x <- chartr("' ", "_", x)
#Error in chartr("' ", "_", "a'b c") : 'old' is longer than 'new'

library(gsubfn)
gsubfn(".", list("'" = "", " " = "_"), x)
# [1] "ab_c"

library(magrittr)

x <- "a'b c"

x %<>%
  gsub("'", "", .) %>%
  gsub(" ", "_", .)
x
##[1] "ab_c"

gsub("\s", "", chartr("' ", " _", x)) # Use whitespace and then remove it