The first thought that came to mind were the religious eunuchs of Anatolian and Scythian cults from the 2nd and 1st centuries BC. But if we want to look for something more secular, we're going to have to go much later in Roman history. (We could glance at some of the eunuchs in the ranks of the likes of Maecenas (Sen. Ep. 114.6) or the fact that Septimius Severus supposedly had a hundred Roman citizens castrated (Cass. Dio. 75.14) - but I wouldn't put much stock in the latter in particular. Not a big fan of Cassius Dio, myself.)

By the 4th century we see a rise in eunuchs in the Roman secular world, which would be me more what you're looking for, I think. Ammianus Marcellinus mentions that a Roman senator's retinue might include "a throng of eunuchs" (Amm. Marc. 14.6.17). But by this time they would have grown out of mere household servants. Lactantius, while certainly not the largest fan of Diocletian, mentions that in Diocletian's reign eunuchs were those "on whom the whole palace and the emperor himself depended" (Lact. DM 15) - Again, I wouldn't look too closely at this, since it would have undoubtedly been used to fling mud at Diocletian's character. (An emperor who relies upon eunuchs to run imperial affairs? For shame).

Still there's an indication that they began to occupy a more central place in the Late Roman court. Usually freed slaves from Armenia or Persia, they formed a close corps of palace attendants headed by the imperial chamberlain, praepositus sacri cubiculi, who as a vir illustris had parity of rank with the leading functionaries of the empire. Under Constantius II the chamberlain Eusebius was accused of running the government (Amm. Marc. 18.4.3); Arcadius' eunuch, Eutropius, rose to be consul in the east in AD 399, and led a military expedition against the Huns; in AD 550 Justinian made his praepositus, Narses, supreme commander in Italy. Their permanent presence made these eunuch-courtiers influential channels of access to the emperor, and greatly enriched them in the process, thus adding resentment to the general distaste which they continued to attract. For late Roman rulers, however, this same social exclusion was a guarantee of loyalty.

Still, I couldn't find anything on other types of mutilation (such as blinding). I imagine that would have been more to exclude people from lines of succession. But that would require more in-depth research, if anyone wants to jump in.

((Note: primary source was the OCD))