There are explicit date formatting options in R (see answer by Greg). Another option would be to separate the date into 3 columns, and then recombine the month and year, putting a / in between. Note this leaves the new date column in character format, which you may want to change depending on your needs.
library(tidyr)
df <- data.frame(date = "13/01/2020")
df <- separate(df, date, into = c("day","month","year"), sep = "/")
df$newdate <- paste(df$month, df$year, sep = "/")
