Here are a couple of ways of doing it.
arr = [1, 2, 3, 3, 4, 4, 5, 6, 6, 6, 7]
#1
b = []
a = arr.dup
while a.any?
  u = a.uniq
  b << u
  a = a.difference u
end
b
  #=> [[1, 2, 3, 4, 5, 6, 7], [3, 4, 6], [6]] 
The helper Array#difference is defined in my answer here.
#2
arr.map { |n| [n, arr.count(n)] }
   .each_with_object({}) { |(n,cnt),h|
     (1..cnt).each { |i| (h[i] ||= []) << n } }
   .values
   .map(&:uniq)
  #=> [[1, 2, 3, 4, 5, 6, 7], [3, 4, 6], [6]]
The steps, for:
arr = [1, 2, 3, 3, 6, 6, 6, 7]
a = arr.map { |n| [n, arr.count(n)] }
  #=> [[1, 1], [2, 1], [3, 2], [3, 2], [4, 2], [4, 2],
  #    [5, 1], [6, 3], [6, 3], [6, 3], [7, 1]] 
enum = a.each_with_object({})
  #=> #<Enumerator: [[1, 1], [2, 1], [3, 2], [3, 2], [4, 2], [4, 2],
  #   [5, 1], [6, 3], [6, 3], [6, 3], [7, 1]]:each_with_object({})> 
To view the elements of enum:
enum.to_a
  #=> [[[1, 1], {}], [[2, 1], {}],...[[7, 1], {}]] 
Now step through the enumerator and examine the hash after each step:
(n,cnt),h = enum.next
    #=> [[1, 1], {}] 
n   #=> 1 
cnt #=> 1 
h   #=> {} 
(1..cnt).each { |i| (h[i] ||= []) << n }
h   #=> {1=>[1]} 
(n,cnt),h = enum.next
  #=> [[2, 1], {1=>[1]}] 
(1..cnt).each { |i| (h[i] ||= []) << n }
h #=> {1=>[1, 2]} 
(n,cnt),h = enum.next
  #=> [[3, 2], {1=>[1, 2]}] 
(1..cnt).each { |i| (h[i] ||= []) << n }
h #=> {1=>[1, 2, 3], 2=>[3]} 
(n,cnt),h = enum.next
  #=> [[3, 2], {1=>[1, 2, 3], 2=>[3]}] 
(1..cnt).each { |i| (h[i] ||= []) << n }
h #=> {1=>[1, 2, 3, 3], 2=>[3, 3]} 
(n,cnt),h = enum.next
  #=> [[6, 3], {1=>[1, 2, 3, 3], 2=>[3, 3]}] 
(1..cnt).each { |i| (h[i] ||= []) << n }
h #=> {1=>[1, 2, 3, 3, 6], 2=>[3, 3, 6], 3=>[6]} 
(n,cnt),h = enum.next
  #=> [[6, 3], {1=>[1, 2, 3, 3, 6], 2=>[3, 3, 6], 3=>[6]}] 
(1..cnt).each { |i| (h[i] ||= []) << n }
h #=> {1=>[1, 2, 3, 3, 6, 6], 2=>[3, 3, 6, 6], 3=>[6, 6]} 
(n,cnt),h = enum.next
  #=> [[6, 3], {1=>[1, 2, 3, 3, 6, 6], 2=>[3, 3, 6, 6], 3=>[6, 6]}] 
(1..cnt).each { |i| (h[i] ||= []) << n }
h #=> {1=>[1, 2, 3, 3, 6, 6, 6], 2=>[3, 3, 6, 6, 6], 3=>[6, 6, 6]} 
(n,cnt),h = enum.next
  #=> [[7, 1], {1=>[1, 2, 3, 3, 6, 6, 6], 2=>[3, 3, 6, 6, 6], 3=>[6, 6, 6]}] 
(1..cnt).each { |i| (h[i] ||= []) << n }
h #=> {1=>[1, 2, 3, 3, 6, 6, 6, 7], 2=>[3, 3, 6, 6, 6], 3=>[6, 6, 6]} 
Lastly, extract and uniqify the values of the hash:
b = h.values
  #=> [[1, 2, 3, 3, 6, 6, 6, 7], [3, 3, 6, 6, 6], [6, 6, 6]]
b.map(&:uniq)
  #=> [[1, 2, 3, 6, 7], [3, 6], [6]]