dplyr issues when using group_by(multiple variables)

I had a similar problem. I found that simply detaching plyr solved it:

detach(package:plyr)    
library(dplyr)

Taking Dickoa's answer one step further -- as Hadley says "summarise peels off a single layer of grouping". It peels off grouping from the reverse order in which you applied it so you can just use

mtcars %>%
 group_by(cyl, gear) %>%
 summarise(newvar = sum(wt)) %>%
 summarise(newvar2 = sum(newvar) + 5)

Note that this will give a different answer if you use group_by(gear, cyl) in the second line.

And to get your first attempt working:

df1 <- mtcars %>%
 group_by(cyl, gear) %>%
 summarise(newvar = sum(wt))

df2 <- df1 %>%
 group_by(cyl) %>%
 summarise(newvar2 = sum(newvar)+5)

If you translate your plyr code into dplyr using summarise instead of mutate you get the same results.

library(plyr)
df1 <- ddply(mtcars, .(cyl, gear), summarise, newvar = sum(wt))
df2 <- ddply(df1, .(cyl), summarise, newvar2 = sum(newvar) + 5)
df2
##   cyl newvar2
## 1   4  30.143
## 2   6  26.820
## 3   8  60.989

detach(package:plyr)    
library(dplyr)
mtcars %.%
    group_by(cyl, gear) %.%
    summarise(newvar = sum(wt)) %.%
    group_by(cyl) %.%
    summarise(newvar2 = sum(newvar) + 5)
##   cyl newvar2
## 1   4  30.143
## 2   8  60.989
## 3   6  26.820

EDIT

Since summarise drops the last group (gear) you can skip the second group_by (see @hadley comment below)

library(dplyr)
mtcars %.%
    group_by(cyl, gear) %.%
    summarise(newvar = sum(wt)) %.%
    summarise(newvar2 = sum(newvar) + 5)
##   cyl newvar2
## 1   4  30.143
## 2   8  60.989
## 3   6  26.820