In tidyverse (w/ lubridate added):
library(tidyverse)
library(lubridate)
dfYrMon <- 
    df1 %>% 
    mutate(date = parse_date_time(month, "my"),
           year = year(date),
           month = month(date)
           ) %>% 
    arrange(year, month) %>% 
    select(date, year, month, result)
With data:
df1 <- tibble(month = c("01/2018", "02/2018", "03/2018", "04/2018", "05/2018", "11/2017", "12/2017"), 
              result = c(96.13636, 96.4, 94, 97.92857, 95.75, 98.66667, 97.78947))
Will get you this 'dataframe':
# A tibble: 7 x 4
        date  year month   result
      <dttm> <dbl> <dbl>    <dbl>
1 2017-11-01  2017    11 98.66667
2 2017-12-01  2017    12 97.78947
3 2018-01-01  2018     1 96.13636
4 2018-02-01  2018     2 96.40000
5 2018-03-01  2018     3 94.00000
6 2018-04-01  2018     4 97.92857
7 2018-05-01  2018     5 95.75000
Making your data values atomic (year in its own column, month in its own column) generally improves the ease of manipulation.
Or if you want to use base R date manipulations instead of lubridate's:  
library(tidyverse)
dfYrMon_base <- 
    df1 %>% 
    mutate(date = as.Date(paste("01/", month, sep = ""), "%d/%m/%Y"),
           year = format(as.Date(date, format="%d/%m/%Y"),"%Y"),
           month = format(as.Date(date, format="%d/%m/%Y"),"%m")
          ) %>%
    arrange(year, month) %>%
    select(date, year, month, result)
dfYrMon_base
Note the datatypes created.
# A tibble: 7 x 4
        date  year month   result
      <date> <chr> <chr>    <dbl>
1 2017-11-01  2017    11 98.66667
2 2017-12-01  2017    12 97.78947
3 2018-01-01  2018    01 96.13636
4 2018-02-01  2018    02 96.40000
5 2018-03-01  2018    03 94.00000
6 2018-04-01  2018    04 97.92857
7 2018-05-01  2018    05 95.75000