In the Name of Allah, the Inspirer of Truth.
Assalamu Alaikum Warahmatullahi Wabarakatuh
This is impermissible.
....Help you one another in AlBirr and AtTaqwa (virtue, righteousness and piety); but do not help one another in sin and transgression. And fear All‚h. Verily, All‚h is Severe in punishment. (Al Quran 5:2)
As Muslims we must ensure our livelihood is Halaal. No person would ever run the risk of drinking sweet tasting poison, because he knows that though it tastes very nice, as he will suffer dire physical effects, if not die from it. Similarly Haraam livelihood weakens our resolve to stay away from evil, and performing good actions, rather this will incline us towards Haraam. Salaah and other good actions if performed, will be performed with reluctance, haste, and bereft of Nuraaniyat (celestial light).
Meat slaughtered not according to Islamic rites is patently impermissible. Such meat is not fit to give to animals. To handle, prepare, sell etc. such meat is not becoming of a Mu'min, and to take it further, is assisting another in sin. Income from such employment is tainted, and far from wholesome.
Whilst we sympathise with your stutter problem, this does not justify earning Haraam. You should get specialist help with the stutter. Consult your GP, who will refer you to a speech therapist. More often that not, stutters (stammer US usage) is due to psychological reasons, which can be bottomed. More importantly, recite in abundance from Surah TaHa, the verses 25,26, and 27 (located in the 16th Para).
Since this is a part time job for extra money, then you should leave this job immediately. If however, this is not the case, and you support a family with this income, and you find it difficult to leave then you must seriously look for another job, whilst making abundant Istighfaar. Leave when you have found something suitable.
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