Energy for regrowth is stored in the roots, so since they are still alive for now, the plant will continue to produce suckers (stems/foliage arising from the root system or trunk stump). If you keep removing suckers promptly, they will eventually exhaust the plant's energy reserves and will stop returning. If allowed to grow for a time before removal, though, the photosynthesis they are performing produces fuel for growth which they can then store in the roots, "recharging the battery," so to speak. Each time it's forced to regrow suckers, that root system battery is losing energy, so sucker removal deprives the plant of the opportunity to feed itself.

A faster work-around would be to carefully apply a systemic herbicide (glyphosate being a commonly-used active ingredient) to the suckers. Avoid contact with any desirable plants in the area as the application can damage them as well. A systemic herbicide is absorbed and moved down into the root system, where it will kill roots to prevent resprouting. Depending on how extensive the root system is and how well-established the tree was (how much energy was stored in roots), repeat herbicide treatments might be needed before the remnants of the plant are fully dead. Always follow product label instructions for application method and timing. If you prefer to avoid chemicals, continued physical removal of the suckers is fine by itself, but expect that the process of exhausting the roots may take longer.

Miri

It might be effective if nothing else desirable is growing too close to the suckers, where they too would be covered up. Suckers might appear growing from roots further from the old trunk, especially if the original group is denied light (and since suckers can arise from almost anywhere along the root system), but if you keep an eye out for them and cut them down as soon as they are discovered, smothering the main clump may be sufficient.

Miri