Use format
to specify the date format you'd like
date <- as.Date("13/01/2020", format = "%d/%m/%Y")
format(date, "%m/%Y")
[1] "01/2020"
Edit - applying to dataframe column
dates <- c("13/01/2020", "17/02/2015", "13/03/2013")
df <- data.frame(dates, stringsAsFactors = FALSE)
df$dates <- as.Date(df$dates, format = "%d/%m/%Y")
df$dates_format <- format(df$dates, "%m/%Y")
df
dates dates_format
1 2020-01-13 01/2020
2 2015-02-17 02/2015
3 2013-03-13 03/2013