Using dplyr, lubridate, and update:

library(dplyr)
library(lubridate)

temp <- as.Date(c("2014-06-01","1993-06-01", "2013-06-03", "1999-01-31"), "%Y-%m-%d")

temp %>%
  update(year = 0) %>%
  format("%m-%d") %>%
  sort()
#> [1] "01-31" "06-01" "06-01" "06-03"