Mina deploy with Puma task, support `start, stop, restart` feature, use `pumactl`. Thanks this tutorial for saving my life: http://ruby-journal.com/how-to-setup-rails-app-with-puma-and-nginx/

deploy.rb

require 'mina/bundler'
require 'mina/rails'
require 'mina/git'
require 'mina/rvm'    # for rvm support. (http://rvm.io)

set :domain, 'deploy@host'
set :repository, 'git...
set :branch, 'master'

set :shared_paths, ['config/database.yml', 'config/application.yml', 'log', 'tmp/sockets', 'tmp/pids']

task :environment do
  set :stage, ENV['to']

  case stage
  when 'production'
    set :rails_env, 'production'
    set :deploy_to, '
    set :start_port, 30xx
  when 'staging'
    set :rails_env, 'staging'
    set :deploy_to, ''
    set :start_port, 30xx
  else
    print_error 'NO environment is specificed'
    exit
  end

  set_default :puma_state, -> { "#{deploy_to}/#{shared_path}/tmp/sockets/puma.state" }
  set_default :puma_pid, ->  { "#{deploy_to}/#{shared_path}/tmp/pids/puma.pid" }

  invoke :'rvm:use[ruby-v@gemset]'
end

task :setup => :environment do
  queue! %[mkdir -p "#{deploy_to}/#{shared_path}/log"]
  queue! %[chmod g+rx,u+rwx "#{deploy_to}/#{shared_path}/log"]

  queue! %[mkdir -p "#{deploy_to}/#{shared_path}/config"]
  queue! %[chmod g+rx,u+rwx "#{deploy_to}/#{shared_path}/config"]

  queue! %[touch "#{deploy_to}/#{shared_path}/config/database.yml"]
  queue! %[touch "#{deploy_to}/#{shared_path}/config/secrets.yml"]
  queue  %[echo "-----> Be sure to edit '#{deploy_to}/#{shared_path}/config/database.yml' and 'secrets.yml'."]

  queue %[
    repo_host=`echo $repo | sed -e 's/.*@//g' -e 's/:.*//g'` &&
    repo_port=`echo $repo | grep -o ':[0-9]*' | sed -e 's/://g'` &&
    if [ -z "${repo_port}" ]; then repo_port=22; fi &&
    ssh-keyscan -p $repo_port -H $repo_host >> ~/.ssh/known_hosts
  ]
end

desc "Deploys the current version to the server."
task :deploy => :environment do
  to :before_hook do
  end
  deploy do
    invoke :'git:clone'
    invoke :'deploy:link_shared_paths'
    invoke :'bundle:install'
    invoke :'rails:db_migrate'
    invoke :'rails:assets_precompile'
    invoke :'deploy:cleanup'

    to :launch do
      invoke :'puma_restart'
    end
  end
end

task :puma_start => :environment do
  queue! %[
    if [ -e '#{puma_pid}' ]; then
      echo 'Puma is already running'
    else
      echo 'Start Puma'
      cd #{deploy_to}/#{current_path} && puma -q -d -e #{rails_env} -C #{deploy_to}/#{current_path}/config/puma.rb -p #{start_port} -S #{puma_state} --pidfile #{puma_pid}
    fi
  ]
end

task :puma_restart => :environment do
  queue! %[
    if [ -e '#{puma_pid}' ]; then
      echo 'Restart Puma'
      cd #{deploy_to}/#{current_path} && pumactl -S #{puma_state} restart
    else
      echo 'Start Puma'
      cd #{deploy_to}/#{current_path} && puma -q -d -e #{rails_env} -C #{deploy_to}/#{current_path}/config/puma.rb -p #{start_port} -S #{puma_state} --pidfile #{puma_pid}
    fi
  ]
end

task :puma_stop => :environment do
  queue! %[
    if [ -e '#{puma_pid}' ]; then
      cd #{deploy_to}/#{current_path} && pumactl -S #{puma_state} stop
      rm #{puma_pid}
    else
      echo 'Puma is not running. Phew!!!'
    fi
  ]
end

There are some changes in the latest version of Mina (1.2):

Ps: I also added the socket flag

# deploy.rb
set :puma_state, "#{fetch(:shared_path)}/tmp/sockets/puma.state"
set :puma_socket, "#{fetch(:shared_path)}/tmp/sockets/puma.sock"
set :puma_pid, "#{fetch(:shared_path)}/tmp/pids/puma.pid"
set :start_port, 3000

task puma_start: :remote_environment do
  command %[
    if [ -e '#{fetch(:puma_pid)}' ]; then
      echo 'Puma is already running'
    else
      echo 'Start Puma'
      cd #{fetch(:current_path)} && bundle exec puma -q -d -e #{fetch(:rails_env)} -C #{fetch(:current_path)}/config/puma.rb -p #{fetch(:start_port)} -S #{fetch(:puma_state)} -b "unix://#{fetch(:puma_socket)}" --pidfile #{fetch(:puma_pid)}
    fi
  ]
end

task puma_restart: :remote_environment do
  command %[
    if [ -e '#{fetch(:puma_pid)}' ]; then
      echo 'Restart Puma'
      cd #{fetch(:current_path)} && bundle exec pumactl -S #{fetch(:puma_state)} restart
    else
      echo 'Start Puma'
      cd #{fetch(:current_path)} && bundle exec puma -q -d -e #{fetch(:rails_env)} -C #{fetch(:current_path)}/config/puma.rb -p #{fetch(:start_port)} -S #{fetch(:puma_state)} -b "unix://#{fetch(:puma_socket)}" --pidfile #{fetch(:puma_pid)}
    fi
  ]
end

task puma_stop: :remote_environment do
  command %[
    if [ -e '#{fetch(:puma_pid)}' ]; then
      cd #{fetch(:current_path)} && bundle exec pumactl -S #{fetch(:puma_state)} stop
      rm #{fetch(:puma_socket)}
      rm #{fetch(:puma_state)}
      rm #{fetch(:puma_pid)}
    else
      echo 'Puma is not running. Phew!!!'
    fi
  ]
end