You can also perform rowwise operations but this is not the preferred method becuse it's "untidy".
orig.DF %>%
group_by(block, plot) %>%
summarise_if(is.numeric, mean) %>%
rowwise() %>%
mutate(mean_1_2 = mean(c(data1,data2)))
#> Source: local data frame [2 x 5]
#> Groups: <by row>
#>
#> # A tibble: 2 x 5
#> block plot data1 data2 mean_1_2
#> <fct> <fct> <dbl> <dbl> <dbl>
#> 1 T1 1 2 2.5 2.25
#> 2 T2 1 3.5 2 2.75
I recommend you to open a new topic about this but providing a relevant REPRoducible EXample (reprex), that way we can better understand the structure of your dataset and provide more suitable help.
If you've never heard of a reprex before, you might want to start by reading this FAQ: