Can you clear MouseButton1Click events from a button gui?

Yes, you can Disconnect connections to an RBXScriptConnection object that was created through a Connect().

local connection = button.MouseButton1Click:Connect(function()
	print("Before disconnecting.")
end)

wait(5) -- waits 5 seconds just for demonstration purposes

connection:Disconnect()

connection = button.MouseButton1Click:Connect(function()
	print("After disconnecting.")
end)

When you initially click, it will print "Before disconnecting." However, after 5 seconds, it will Disconnect() the MouseButtonClick connection, and the new Connect()'s function definition will make it print "After disconnecting."