df <- data.frame(Q1 = c(1, 2, 1, 4), Q2 = c(4, 2, 3, 1), Q3 = c(3, 3, 2, 3),
             Q4 = c(4, 4, 2, 4), Q5 = c(4, 2, 3, 1), Q6 = c(7, 2, 3, 1))

library(dplyr)

df$mean <- df %>%
  select(Q1, Q2, Q3) %>%
  mutate_all(funs(. - 1)) %>%
  apply(1, function(x) {
    round(mean(x[!is.na(x) & x != 3]), digits = 2)
  })

df <- df %>%
  select(Q1, Q2, Q3) %>%
  mutate_all(funs(. - 1)) %>%
  mutate(mean = apply(., 1, function(x)
    round(mean(x[!is.na(x) & x != 3]), digits = 2)))

subtract <- c("Q1", "Q2", "Q3")
df2 <- df %>%
  mutate_at(subtract, funs(. - 1)) %>%
  mutate(mean = apply(select(., one_of(subtract)), 1, function(x)
    round(mean(x[!is.na(x) & x != 3]), digits = 2)))

df2
#   Q1 Q2 Q3 Q4 Q5 Q6 mean
# 1  0  3  2  4  4  7 1.00
# 2  1  1  2  4  2  2 1.33
# 3  0  2  1  2  3  3 1.00
# 4  3  0  2  4  1  1 1.00

library(tidyverse)

df %>%
  select(1:3) %>%
  mutate_all(funs(. - 1)) %>%
  rowwise() %>%
  do( (.) %>% as.data.frame %>%
      mutate(mean = mean(.[. != 3], na.rm = TRUE)))

#    Q1    Q2    Q3  mean
#* <dbl> <dbl> <dbl> <dbl>
#1  0     3.00  2.00  1.00
#2  1.00  1.00  2.00  1.33
#3  0     2.00  1.00  1.00
#4  3.00  0     2.00  1.00

(df[1:3] - 1) %>%
    rowwise() %>%
    do( (.) %>% as.data.frame %>%
    mutate(mean = mean(.[. != 3], na.rm = TRUE)))

apply_fun <- function(x) {
  mean(x[x != 3], na.rm = TRUE)
}

(df[1:3] - 1) %>%
  rowwise() %>%
  mutate(mean = apply_fun(c(Q1, Q2, Q3)))

 #    Q1    Q2    Q3  mean
 #  <dbl> <dbl> <dbl> <dbl>
 #1  0     3.00  2.00  1.00
 #2  1.00  1.00  2.00  1.33
 #3  0     2.00  1.00  1.00
 #4  3.00  0     2.00  1.00