Mutate multiple variable to create multiple new variables

Because you are operating on column names, you need to use mutate_at rather than mutate_if which uses the values within columns

tb %>% mutate_at(vars(starts_with("y")), funs(. - z))
#> # A tibble: 3 x 5
#>       x    y1    y2    y3     z
#>   <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1     1     0     2     4     2
#> 2     2    -2    -1     0     3
#> 3     3     5     3     1     1

To create new columns, instead of overwriting existing ones, we can give name to funs

# add suffix
tb %>% mutate_at(vars(starts_with("y")), funs(mod = . - z))
#> # A tibble: 3 x 8
#>       x    y1    y2    y3     z y1_mod y2_mod y3_mod
#>   <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>
#> 1     1     2     4     6     2      0      2      4
#> 2     2     1     2     3     3     -2     -1      0
#> 3     3     6     4     2     1      5      3      1

# remove suffix, add prefix
tb %>%
  mutate_at(vars(starts_with("y")),  funs(mod = . - z)) %>%
  rename_at(vars(ends_with("_mod")), funs(paste("mod", gsub("_mod", "", .), sep = "_")))
#> # A tibble: 3 x 8
#>       x    y1    y2    y3     z mod_y1 mod_y2 mod_y3
#>   <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>
#> 1     1     2     4     6     2      0      2      4
#> 2     2     1     2     3     3     -2     -1      0
#> 3     3     6     4     2     1      5      3      1

Edit: In dplyr 0.8.0 or higher versions, funs() will be deprecated (source1 & source2), need to use list() instead

tb %>% mutate_at(vars(starts_with("y")), list(~ . - z))
#> # A tibble: 3 x 5
#>       x    y1    y2    y3     z
#>   <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1     1     0     2     4     2
#> 2     2    -2    -1     0     3
#> 3     3     5     3     1     1

tb %>% mutate_at(vars(starts_with("y")), list(mod = ~ . - z))
#> # A tibble: 3 x 8
#>       x    y1    y2    y3     z y1_mod y2_mod y3_mod
#>   <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>
#> 1     1     2     4     6     2      0      2      4
#> 2     2     1     2     3     3     -2     -1      0
#> 3     3     6     4     2     1      5      3      1

tb %>%
  mutate_at(vars(starts_with("y")),  list(mod = ~ . - z)) %>%
  rename_at(vars(ends_with("_mod")), list(~ paste("mod", gsub("_mod", "", .), sep = "_")))
#> # A tibble: 3 x 8
#>       x    y1    y2    y3     z mod_y1 mod_y2 mod_y3
#>   <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>
#> 1     1     2     4     6     2      0      2      4
#> 2     2     1     2     3     3     -2     -1      0
#> 3     3     6     4     2     1      5      3      1

Edit 2: dplyr 1.0.0+ has across() function which simplifies this task even further

Basic usage

across() has two primary arguments:

• The first argument, .cols, selects the columns you want to operate on. It uses tidy selection (like select()) so you can pick variables by position, name, and type.

• The second argument, .fns, is a function or list of functions to apply to each column. This can also be a purrr style formula (or list of formulas) like ~ .x / 2. (This argument is optional, and you can omit it if you just want to get the underlying data; you'll see that technique used in vignette("rowwise").)

# Control how the names are created with the `.names` argument which 
# takes a [glue](http://glue.tidyverse.org/) spec:
tb %>% 
  mutate(
    across(starts_with("y"), ~ .x - z, .names = "mod_{col}")
  )
#> # A tibble: 3 x 8
#>       x    y1    y2    y3     z mod_y1 mod_y2 mod_y3
#>   <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>
#> 1     1     2     4     6     2      0      2      4
#> 2     2     1     2     3     3     -2     -1      0
#> 3     3     6     4     2     1      5      3      1

tb %>% 
  mutate(
    across(num_range(prefix = "y", range = 1:3), ~ .x - z, .names = "mod_{col}")
  )
#> # A tibble: 3 x 8
#>       x    y1    y2    y3     z mod_y1 mod_y2 mod_y3
#>   <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>
#> 1     1     2     4     6     2      0      2      4
#> 2     2     1     2     3     3     -2     -1      0
#> 3     3     6     4     2     1      5      3      1

### Multiple functions
tb %>% 
  mutate(
    across(c(matches("x"), contains("z")), ~ max(.x, na.rm = TRUE), .names = "max_{col}"),
    across(c(y1:y3), ~ .x - z, .names = "mod_{col}")
  )
#> # A tibble: 3 x 10
#>       x    y1    y2    y3     z max_x max_z mod_y1 mod_y2 mod_y3
#>   <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>
#> 1     1     2     4     6     2     3     3      0      2      4
#> 2     2     1     2     3     3     3     3     -2     -1      0
#> 3     3     6     4     2     1     3     3      5      3      1

^{Created on 2018-10-29 by the reprex package (v0.2.1)}