It's in the rowwise vignette, but it's an unusual approach, and, at least for me, a confusing one. Normally, one uses summarise to collapse a data frame down to a smaller number of rows while generating summary values (counts, averages, etc.) and mutate to add columns to a data frame without changing the rest of the data frame.
In the code below, the first example is from your question and parallels the rowwise vignette. The second example is what I think would be considered the "typical" way of achieving the same goal.
library(palmerpenguins)
library(tidyverse)
penguins %>%
rowwise() %>%
summarize(species, island,
sum_mm = bill_length_mm + flipper_length_mm)
penguins %>%
mutate(sum_mm = bill_length_mm + flipper_length_mm) %>%
select(species, island, sum_mm)