If surgery is done while a child is learning to speak, will it cause stuttering?

No. There is no evidence that tongue-tie surgery causes stuttering; if anything, freer tongue movement helps in learning sounds made with the tongue. For a few days right after surgery a child may speak less because of pain and the unfamiliar feeling, but that resolves naturally once the wound heals. Surgery alone does not correct speech habits that are already established, though, so for a child with a clear speech problem, combining surgery with speech therapy helps.