I'm inferring that when you say "is not working", it's because the percent sign is being removed:
separate(data_frame(a=c("45 (10, 89)","34")), a, c('x','y','z'), extra="drop")
# Warning: Too few values at 1 locations: 2
# # A tibble: 2 × 3
#       x     y     z
# * <chr> <chr> <chr>
# 1    45    10    89
# 2    34  <NA>  <NA>
separate(data_frame(a=c("45% (10, 89)","34%")), a, c('x','y','z'), extra="drop")
# Warning: Too few values at 1 locations: 2
# # A tibble: 2 × 3
#       x     y     z
# * <chr> <chr> <chr>
# 1    45    10    89
# 2    34        <NA>
From ?separate:
separate(data, col, into, sep = "[^[:alnum:]]+", remove = TRUE,
  convert = FALSE, extra = "warn", fill = "warn", ...)
...
Since you are not overriding the default of sep, it finds anything that is not a letter or a number. FYI, [^[:alnum:]]+ is analogous to [^A-Za-z0-9]+, which matches "1 or more characters that are not in the character-ranges of A-Z, a-z, or 0-9".
Simply provide a more-detailed sep, and you'll get what you want.
separate(data_frame(a=c("45% (10, 89)","34%")), a, c('x','y','z'), sep="[^[:alnum:]%]+", extra="drop")
# Warning: Too few values at 1 locations: 2
# # A tibble: 2 × 3
#       x     y     z
# * <chr> <chr> <chr>
# 1   45%    10    89
# 2   34%  <NA>  <NA>
Edit: using your most recent sample data:
separate(data_frame(a=c("45% (10/89)","34%","","67%","78% (89/98)")), a, c('x','y','z'), sep="[^[:alnum:]%]+", extra="drop")
# Warning: Too few values at 3 locations: 2, 3, 4
# # A tibble: 5 × 3
#       x     y     z
# * <chr> <chr> <chr>
# 1   45%    10    89
# 2   34%  <NA>  <NA>
# 3        <NA>  <NA>
# 4   67%  <NA>  <NA>
# 5   78%    89    98