It looks to me like the issue is in your date conversion. See below for an approach to converting the strings to dates using the lubridate package. As an aside, you may want to think about reshaping your data from wide to long before you plot it -- in general, ggplot2 works much better with long instead of wide data.
library(tidyverse)
library(lubridate)
swd <- read_csv(url("https://api.covid19india.org/csv/latest/state_wise_daily.csv"))
swc <- swd %>%
filter(Status == "Confirmed") %>%
mutate(Date = dmy(Date))
ggplot(swc, aes(x = Date)) +
geom_line(aes(y = MH, color = "darkred")) +
geom_line(aes(y = GJ, color = "steelblue")) +
geom_line(aes(y = TN, color = "yellow")) +
geom_line(aes(y = RJ, color = "green")) +
geom_line(aes(y = DL, color = "orange")) +
geom_line(aes(y = UP, color = "pink")) +
geom_line(aes(y = MP, color = "red")) +
geom_line(aes(y = WB, color = "blue")) +
geom_line(aes(y = BR)) +
geom_line(aes(y = KL, color = "teal"))