One or more of the fuel lines may have developed a leak as well. You should replace the fuel line with a new one instead of attempting to repair the old line.
The primer bulb draws fuel through the carburetor when pushed to prime the engine when first starting. Over time, the rubber can become brittle and crack, causing the bulb to leak gas. Installing a new primer bulb will fix the problem.
If the leak appears to be coming from the carburetor, it is likely that the carburetor bowl gasket is worn out or missing. You can replace the gasket with a new one to solve the problem.
Various float assembly components inside the carburetor bowl can be defective as well. The float needle opens and closes the float valve to allow fuel to enter the bowl. If the float needle or the float itself is damaged, the carburetor may continue to fill with the fuel until it overflows. You should be able to stop the leaking by replacing one or more of these components.
The problem the mower fuel tank could be damaged as well. If the tank has a crack or a small hole, you should replace it instead of trying to repair it.