The Water Supply Department collects your water usage fees and also waste disposal fees, but if you have hired a private company to dispose of your garbage, you can ask the Water Supply Department not to collect your garbage disposal fees.

一般事業廢棄物如已委託民營清除處理機構清理，而未辦理停徵自來水代徵清除處理費者，請逕向本局環境衛生管理科辦理，有關辦理停徵隨自來水代徵清除處理費應檢具資料，請逕至本局網站
If you have hired a private waste management company to manage the disposal of your garbage, and you have not requested the Water Supply Department to discontinue the collection of garbage disposal fees, please have it done at the Environment Hygiene Management Office of this department. As to the documents needed to make such a request, please visit our department website.

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Note added at 10 hrs (2021-12-09 05:01:34 GMT)
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Translations related to the context that I found in a Taiwanese government website:
一般事業廢棄物: general industrial waste.
民營清除處理機構: private waste clearance and disposal organization
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一、甲級：從事一般廢棄物、一般事業廢棄物及有害事業廢棄物處理業務
；應置專任乙級以上處理技術員二人，其中甲級處理技術員至少一人
https://oaout.epa.gov.tw/law/EngLawContent.aspx?lan=C&id=279

I. Grade A Organizations: Engage in the disposal of general waste, general industrial waste, and hazardous industrial waste. They shall hire two full-time disposal technicians of Grade B or above, of whom at least one is a Grade A disposal technician.
https://oaout.epa.gov.tw/law/EngLawContent.aspx?lan=E&id=279