All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
In principle, full images of animate beings (human or animal) are forbidden. This view is based on several narrations prohibiting images. For example, the Messenger of Allah (Peace and blessings be upon him) said: "The makers of these pictures will be punished on the Day of Resurrection and it will be said to them, 'Make alive what you have created." {Related by Bukhari}.
However, children`s cups with embossed images are excluded from this prohibition. This is attested to in the following narration: " ‘A’isha said: I was playing with dolls in the Prophet’s house and I had companions who played with me; but when God’s Messenger entered they would withdraw from him. He would then send them to me and they would play with me. (Bukhari and Muslim).
Commenting on the Hadith of A`isha, Judge Eyad said: "It indicates that it is permissible to play with dolls, they are excluded from the prohibition, and they train girls to do housework and take care of children. He added that scholars have allowed buying and selling them (dolls)." {Shareh An-Nawawi Ala Muslim, P.397}.
The person who has things-used for mean service-on which prohibited images of animate beings are printed to use them, such as cups and garments. However, honoring these things and using them for ornament isn`t permitted, so he/she can`t continue keeping them.
It is stated in the Shafie book , {Tohfat al-Mohtaj Shareh Al-Minhaj, vol.7:P.433}:"It is permissible to go to a place where there are images on the ground, on a carpet stepped on, or a pillow slept on or a plate eaten from, or a jug, because they are used for mean service. This indicates that images put on a high place or used as ornament are forbidden…………".
In conclusion, in principle, it isn`t permissible to draw pictures of human beings or animals on cups where it could be felt that they can live in that form. Whoever buys such cups to be used for mean service, like drinking, is allowed to keep them while keeping them for ornament is forbidden. And Allah the Almighty knows best.