In my opinion swearing at a child in a nasty way is abusive.
If they say stuff that is rude or call you bad names with swearing like F off you F C *** or I'll f'in kill you ***** that's verbal abuse.
If they say I don't love you and I never did, I hate you, I never wanted you, I wish you were dead, you are ugly as sin, I can't believe your mine, the hospital must have got the baby confused, that's emotional abuse. They can do them both together of course. Some will say things like they are going to lock you up for a year, take all your belongings off you for good, never let you go anywhere again - well it's pretty obviously an exaggeration but it's still very emotionally upsetting for the child.
Parents should discipline a child in a calm way not lash out in anger where they may say things they'll later regret or over punish them.
Of course there is a verbal side to even worse abuse such as physical or sexual abuse. If the parent makes threats of violence towards the child they child may not know if they will follow through or not and be terrified. If the parent has in the past done these things the child will be even more terrified this is about to happen again. That would apply to threats of cigarette burns, hot water scalds, sex, tying them up, smacking or whipping them, forcing them to do all the household chores and refuse to give them enough decent food to live on. Threats of killing the child or killing anyone they tell or killing their pet animal can also be considered abuse. Threats of locking them in cupboards for hours is another one considerd abusive.
Do you want to share what your mum has said to you for us to judge?