You have the right not to pay for a service you're not receiving - that's a basic consumer rule, but management companies rarely voluntarily agree to lower payments. The key thing is not just to stop paying in silence: that can lead to fines and debt. You need to document everything and officially demand a recalculation.
Write a complaint to the management company in two copies - send one by registered mail and bring the other in person, asking for a receipt. Include exact dates when the garbage chute broke, attach photos of the broken hatch, describe how you're disposing of trash on your own. The main thing - demand either full repairs by a specific date, or a payment reduction proportional to the period the service wasn't working. You can specify what percentage you're reducing the amount of garbage you give to the management company (by your logic - 100%, if you're not using it at all).
If the management company ignores you or refuses, you can file a complaint with the supervisory management organization (if one exists in your region) or the housing inspection. At the same time, collect any documents you can: statements from neighbors, video of the broken chute, correspondence with the management company. By the way, my building had a similar situation with the heating system - it "worked" according to the meters, but half the winter our apartments were around 15 degrees. As soon as we filed an official complaint with an overpayment calculation, the management company started looking into it way faster 😅