If you put household waste and garden waste, separately, outside your house for collection once a week (for example), you would say "My household waste and garden waste are collected on a Tuesday". You can omit the first "waste and", leaving "My household and garden waste are collected on a Tuesday" and it would mean the same.
"My household and garden waste is collected on a Tuesday" suggests to me that you put the two sorts of waste into one bag and that one bag is collected.